Transpeaknet for solvent-aware 2d nmr prediction via multi-task pre-training and unsupervised learning

ABSTRACT Nuclear Magnetic Resonance (NMR) spectroscopy is essential for revealing molecular structure, electronic environment, and dynamics. Accurate NMR shift prediction allows researchers

to validate structures by comparing predicted and observed shifts. While Machine Learning (ML) has improved one-dimensional (1D) NMR shift prediction, predicting 2D NMR remains challenging

due to limited annotated data. To address this, we introduce an unsupervised training framework for predicting cross-peaks in 2D NMR, specifically Heteronuclear Single Quantum Coherence

(HSQC). Our approach pretrains an ML model on an annotated 1D dataset of 1H and 13C shifts, then finetunes it in an unsupervised manner using unlabeled HSQC data, which simultaneously

generates cross-peak annotations. Our model also adjusts for solvent effects. Evaluation on 479 expert-annotated HSQC spectra demonstrates our model’s superiority over traditional methods

(_ChemDraw_ and _Mestrenova_), achieving Mean Absolute Errors (MAEs) of 2.05 ppm and 0.165 ppm for 13C shifts and 1H shifts respectively. Our algorithmic annotations show a 95.21%

concordance with experts’ assignments, underscoring the approach’s potential for structural elucidation in fields like organic chemistry, pharmaceuticals, and natural products. SIMILAR

CONTENT BEING VIEWED BY OTHERS TOWARD A UNIFIED BENCHMARK AND FRAMEWORK FOR DEEP LEARNING-BASED PREDICTION OF NUCLEAR MAGNETIC RESONANCE CHEMICAL SHIFTS Article 28 March 2025 RAPID PROTEIN

ASSIGNMENTS AND STRUCTURES FROM RAW NMR SPECTRA WITH THE DEEP LEARNING TECHNIQUE ARTINA Article Open access 18 October 2022 THE 100-PROTEIN NMR SPECTRA DATASET: A RESOURCE FOR BIOMOLECULAR

NMR DATA ANALYSIS Article Open access 04 January 2024 INTRODUCTION Nuclear magnetic resonance (NMR) spectroscopy has emerged as a versatile tool with widespread applications across diverse

scientific domains, including chemistry, environmental science, food science, material science, and drug discovery by unraveling molecular dynamics and structures1,2,3,4. The primary

information of an NMR spectrum arises from the chemical shift, which is determined by the local environment of a nucleus and influenced by interactions through chemical bonds and space. This

mechanism yields unique “fingerprints” corresponding to diverse functional groups or molecular motifs, thereby facilitating the streamlined deduction of atomic connectivity and arrangement.

Interpreting NMR spectra requires following essential guidelines, often referred to as “rules of thumb”, where specific chemical shifts are associated with distinctive functional groups5.

The determination of molecular structures from varying chemical shifts on NMR spectra generally requires the expertise of experienced organic chemists. To facilitate the interpretation of

NMR spectra, significant efforts have been directed towards computational simulation of NMR spectra6. Early computational approaches, like the Hierarchically Ordered Spherical Environment

(HOSE) codes7, aim to encapsulate atom neighborhoods in concentric spheres, utilizing a nearest-neighbor approach to predict NMR shift values. A recent HOSE approach8 yields Mean Absolute

Errors (MAEs) of 3.52 ppm for 13C NMR and 0.29 ppm for 1H NMR on the nmrshiftdb29 dataset. Concurrently, significant efforts have been devoted to the ab initio calculation of NMR

properties.10,11 Density Functional Theory (DFT)-based methods were developed for certain small organic molecules, achieving MAEs of 2.9 ppm for 13C NMR and 0.23 ppm for 1H NMR12. However,

the accuracy of these DFT-based methods relies heavily on the choice of the basis functions, which often require meticulous case-by-case manual tuning for each molecule. Moreover, the

time-intensive nature of DFT calculations limits their applications to comprehensive and large datasets. Recently, the rise of Graph Neural Networks (GNN) and their successes in predicting

molecular properties13,14,15,16,17 has prompted initiatives to employ GNNs for predicting peaks in NMR spectra5,18,19. The application of GNN to molecules is intuitive, as a molecular

structure can be naturally represented as a graph, with each atom as a node and its chemical bonds as edges. On 1D NMR data, a GNN-based model achieves MAEs of 1.355 ppm for 13C NMR and

0.224 ppm for 1H NMR on the nmrshiftdb2 dataset18. While considerable efforts have been made in developing predictive models for 1D NMR, the prediction of 2D NMR remains underexplored.

Heteronuclear Single Quantum Coherence (HSQC) spectroscopy20, a sophisticated 2D NMR technique, is an important tool for elucidating atomic connectivity within complex molecules where

conventional 1D NMR may prove insufficient21,22. By correlating the chemical shifts of hydrogen nuclei with those of heteronuclear nuclei, typically carbon or nitrogen, via scalar coupling

interactions, HSQC facilitates the comprehensive mapping of interatomic connections within a molecule. This mapping yields crucial insights into chemical bonding, molecular conformation, and

intramolecular interactions. As molecular structures become more complex, 1D NMR spectra tend to display increasingly overlapping peaks, making 2D NMR techniques such as HSQC essential for

elucidating local structures. A notable stride in this domain utilizes the ML approach to establish correlations between DFT-simulated HSQC spectra and empirical data to identify

molecules23. However, the accurate prediction of HSQC spectra using ML techniques remains elusive, primarily due to the scarcity of large-scale, high-quality datasets, as well as the

labor-intensive and time-consuming peak annotation process. While numerous annotated 1D spectra are available for training ML models, combining these results to reliably generate 2D NMR data

is far from straightforward. As an example, a recent study introduced a method to integrate the state-of-the-art predictions of proton and carbon 1D spectra into HSQC spectra24, achieving

MAEs of 0.16 ppm for 1H and 2.64 ppm for 13C. This study highlights the inherent difficulties in accurately predicting 2D NMR chemical shifts, as even though the selected 1D NMR models and

methods achieve low error individually, such success cannot be transferred to HSQC cross-peak prediction. Moreover, beyond the challenge of prediction, associating each HSQC peak with its

corresponding local molecular structure is an inevitable task that requires expert domain knowledge and is often time-consuming. Proper calibration is typically necessary to ensure precise

alignment between 1D and HSQC data before interpreting the HSQC spectra. In light of the aforementioned challenges and opportunities in interpreting HSQC spectra, we propose TRANSPEAKNET: a

Transfer learning-based Peak prediction and assignment with unsupervised learning, illustrated in Fig. 1. This framework enables end-to-end training and testing on experimental data. Once

trained, the TransPeakNet model generates cross-peak predictions directly from a SMILES representation and the solvent environment used in the experiment. Additionally, it simultaneously

associates each cross-peak signal with its corresponding carbon-proton pairs. Alongside a Graph Neural Network (GNN) module capturing structural nuances, the model incorporates a solvent

encoder to effectively account for the impact of solvent environments on chemical shifts, which is essential for delivering accurate cross-peak prediction and peak assignment of HSQC

spectra. To tackle the lack of annotated HSQC data, we designed a two-step transfer learning process. First, the model is pre-trained on a labeled 1D NMR dataset via Multi-Task pre-Training

(MTT), enabling it to learn a wide range of C–H interactions. Then, we implement an unsupervised learning strategy that uses the unlabeled HSQC dataset to refine the model’s ability to

accurately discern and label HSQC cross peaks. The model is pre-trained using  ~24,000 annotated 1D NMR dataset from NMRShiftDB29, and finetuned on  ~19,000 experimental HSQC spectra from

HMDB25 and CH-NMR-NP26. The model is thoroughly evaluated and compared to traditional tools like _ChemDraw_27 and _Mestrenova_28 using expert-annotated test datasets. On test dataset, the

model achieves MAEs of 2.05 ppm and 0.165 ppm for 13C shifts and 1H shifts respectively. We also demonstrate that our model effectively considers the impact solvent has on chemical shift,

when making the prediction. When compared with the traditional tools, our model shows promising improvements, especially as the molecular size becomes larger. RESULTS PERFORMANCE ON HSQC

CROSS PEAK PREDICTION AND ASSIGNMENT Figure 2 summarizes the performance of our model on the tasks of HSQC cross-peak prediction and peak assignment, using an expert-annotated test dataset

consisting of 500 molecules, with an average molecular weight of 398.98 Da., and an average number of 56.32 atoms. The annotation process involved three experienced experts with extensive

knowledge in organic chemistry. For each molecule, two experts independently linked the observed cross-peaks from experiments to C–H bonds. If they agreed, the annotation was finalized. In

cases of disagreement, the third expert reviewed and validated the annotations. Samples with poor quality, such as those with insufficient experimental resolution, were excluded from the

test dataset for model evaluation, resulting in 479 high-quality annotations. For chemical shift prediction, our model achieved an MAEs of 2.05 ppm for 13C shifts and 0.16 ppm for 1H shifts.

In terms of annotation accuracy, our model accurately annotated all peaks in 456 out of 479 molecules (95.21%). An example of the model prediction and annotation of a small molecule is

visualized in Fig. 2C for simplicity. Additional examples for medium and large molecules are included in Supplementary Information Section 1, Supplementary Figs. 1–4. For those 23 molecules

that our algorithmic annotations do not fully agree with the experts, 81.56% of the peak annotations still align. Examples of partially correct annotations are visualized in Supplementary

Information Section 2, Supplementary Figs. 5–9. Notably, the peak assignment algorithm operates without a shift discrepancy threshold, allowing it to align all ground truth peaks with

predictions. Given the low MAE of the predicted shifts (2.05 ppm for 13C and 0.165 ppm for 1H), the model provides a solid foundation for accurate assignment. Even in rare cases where a few

atoms in a molecule have relatively large prediction errors, the annotation remains reliable, highlighting its robustness. To evaluate our model’s ability to capture solvent effects, we

tested different solvent encoders for carbon and hydrogen atoms. Empirical results indicate that a solvent encoder with a dimension of 32 is most effective at capturing proton shifts, while

adding additional embeddings for carbon does not yield significant benefits. This partially aligns with expert expectations, as protons are known to be more sensitive to their solvent

environment due to their high exposure to the surrounding molecular environment. By contrast, carbon atoms are less directly influenced by solvent interactions, as they are more deeply

embedded within the molecular structure and shielded by surrounding electron clouds. Additionally, carbon atoms are not directly involved in hydrogen bonding, and their larger mass and lower

sensitivity to external magnetic fields make their shifts less responsive to subtle solvent changes. Furthermore, since the 1D NMR data used for pre-training does not include solvent

information, and some solvent groups (e.g., benzene, acid, etc.) in the HSQC data are underrepresented, as shown in Fig. 3A, the influence of solvent on carbon shifts may be too subtle to

capture at this stage. This remains as our ongoing area of investigation for further insights. To assess the effect of solvents on proton shifts, we report model performance using the true

experimental solvent, a random solvent condition, and the “unknown” solvent condition, with the comparison shown in Fig. 3B. The results demonstrate that using the correct solvent input

yields the lowest prediction error, aligning most closely with experimental observations. This improvement in prediction is particularly significant for the CCl3, DMSO, and methanol solvent

classes, likely due to their prominent presence in the dataset. The effect of water, on the other hand, despite constituting only 1.02% of the data, can be effectively captured by the

solvent encoder. This could be explained by water’s similarity to methanol in its behavior as a hydrogen-bond donor or acceptor. Both solvents can strongly deshield protons in solutes,

causing their NMR peaks to shift higher. The predictability of these hydrogen-bonding interactions may enable the model to generalize well, even with relatively few training examples for

water. These findings underscore the promise of incorporating solvent environments into peak prediction models and highlight the need for more high-quality data with solvent information.

COMPARISON WITH TRADITIONAL TOOLS In organic chemistry, simulating HSQC spectra is crucial for analyzing experimental HSQC spectra, as it assists researchers in assigning the observed cross

peaks to the C–H bonds in target molecules. Traditional approaches, including software solutions such as _ChemDraw_27, and _Mestrenova_28, have long served as the primary resources for this

task. We compared our model with _ChemDraw_ and _Mestrenova_ and the results are shown in Fig. 4, which clearly demonstrate the superiority of our model. It is labor intensive to align

predictions from these traditional tools with ground truth. Moreover, these tools could yield unstable predictions as molecular size and complexity increases. Hence, we randomly selected 150

peaks across different molecular weight categories for comparison. Because the HSQC prediction is not inherently implemented in _ChemDraw_, the cross peaks were constructed and assigned

using 1D predictions (13C and 1H chemical shifts) based on bond connectivity. We also provided two examples with different molecular sizes to visualize the comparison. PERFORMANCE BY

SEGMENTATION To comprehensively evaluate the robustness and generalizability of our model, we conducted a segmentation analysis in the test dataset, assessing its performance across various

molecular subcategories. Segmentation is crucial in this context because it allows us to determine whether the model performs consistently well across diverse molecular characteristics,

rather than excelling in only a specific subset. We selected categories based on molecular weight and the presence of saccharides. These categories were chosen because NMR prediction gets

increasingly challenging as the molecule gets larger, while saccharides represent a distinct chemical group with unique structural features. By examining the model’s performance within these

defined segments, we aim to demonstrate its universal applicability and robustness across a wide range of molecular types. Molecular Weight (MW) is a general indicator of a molecule’s

complexity, encompassing varied geometries, bonding patterns, and the presence of isomers. These factors contribute to increased intramolecular interactions, resulting in spectral complexity

such as closely spaced peaks or overlapping signals. Additionally, the increased number of spin-spin interactions within larger molecules necessitates more advanced NMR techniques to

achieve sufficient resolution29. Furthermore, solubility issues can lead to weak signals, further complicating spectral analysis. Consequently, interpreting HSQC spectra for medium and large

molecules is challenging. Therefore, there is a pressing need for a model that can effectively predict and analyze HSQC spectra for these complex molecules. Figure 5A showcases the

stratified performance on this category, where the test molecules are grouped into three categories: small (MW < 500 daltons), medium (500 <= MW < 1000 daltons), and large (1000

daltons <= MW). On the task of predicting 1H shifts of HSQC cross peaks, the model performs comparably across all groups, achieving excellent MAE of 0.16–0.19 ppm. On the task of

predicting 13C shifts, the model achieves an MAE of 1.93 ppm for medium-sized molecules. Our model demonstrates a good generalization power on large molecules and achieves an MAE of 2 ppm on

predicting 13C shifts for this category, despite the training data containing only a small proportion of large molecules (~2%). Saccharides, or carbohydrates, play critical roles in various

biological processes involved in energy source and storage, cell signaling, cell adhesion, cell recognition, structural integrity of cells and tissues, as well as cognitive functions and

metabolic regulation30,31,32,33. Despite their importance, elucidating the structures of saccharides is challenging due to their inherent structural complexity and diversity. This complexity

arises from the diverse arrangements of monosaccharide units, varied anomeric configurations, and variable glycosidic linkages. Additionally, carbohydrates often lack the crystallinity

required for high-resolution X-ray diffraction, unlike the well-defined crystalline structures of small molecules or proteins. Consequently, NMR spectroscopy, particularly through techniques

such as HSQC, has emerged as an indispensable tool in unraveling the detailed structures of carbohydrates34,35. Forecasting HSQC cross peaks and aligning them with experimental data can

assist in comprehending saccharide connectivity and stereochemistry, thus aiding in structural determination. Our model demonstrates excellent performance in predicting HSQC cross peaks for

saccharides molecules, yielding MAEs of 1.78 for 13C shifts and 0.16 for 1H shifts (see Fig. 5(B)). This level of accuracy is consistent with the overall model performance, which

demonstrates the model’s robustness in handling complex saccharide structures. Figure 6 shows the performance of our model on a few exemplar saccharides. These saccharides feature multiple

ring structures and numerous stereogenic centers, contributing to the intricate nature of their HSQC spectra. Despite these inherent complexities, our model exhibits high accuracy in

predicting the HSQC cross peaks for these molecules. This robust performance underscores our model’s capacity to navigate the complexities associated with saccharides, thereby emphasizing

its versatility and effectiveness across various applications in the field. EFFECTS OF PRE-TRAINING AND FINE-TUNING After pre-trained via MTT on the 1D NMR dataset, the model achieved the

validation performance with MAEs of 0.210 ppm for 1H NMR prediction and 2.228 ppm for 13C NMR prediction. This success can be attributed to MTT which allows the model to effectively learn

atomic latent features as well as local structural information by simultaneously performing 1H and 13C NMR shift predictions. This helps us surpass the problem with limited annotated HSQC

data. However, when directly deploying the pre-trained model on HSQC test dataset, the model MAEs increase to 1.397 ppm and 2.822 ppm for 1H and 13C shifts, respectively. These relatively

large MAEs are expected as the data distribution of the HSQC dataset (76.34% small molecules and 90.33% non-saccharides) differs significantly from that of the 1D NMR dataset (98.80% small

molecules and 99.95% non-saccharides). In addition, the HSQC cross peaks involve interactions beyond simple pairings of 1D 13C and 1H shifts, requiring a deeper understanding of interactions

between atoms. Finally, the frequent absence of solvent labels in the 1D NMR dataset prevents the model from learning solvent effects. Nevertheless, the pre-training via MTT offers a robust

foundation for fine-tuning the model via unsupervised transfer learning. With each iteration, we observed a reduction in model errors. The performance improvement is more pronounced during

the initial iterations and gradually diminishes. By the fifth iteration, the improvement became marginal, indicating the convergence of fine-tuning. Finally, the fine-tuned model achieves

MAEs of 0.165 ppm and 2.05 ppm for 1H and 13C shifts, respectively. Throughout the transfer learning process, the model was trained to gain a more profound understanding of solvent effects

and complex C–H interactions due to intricate molecular structures. DISCUSSION In this study, we introduce a framework to develop machine learning techniques for predicting C–H cross peaks

in HSQC spectra, The framework enables us to tackle two major challenges in this avenue. The first challenge is the scarcity of annotated HSQC data for training machine learning models. The

second challenge is that collecting large volumes of annotated HSQC data is labor-intensive and requires highly trained personnel. In implementing our framework, we developed a model

combining a GNN with a solvent encoder. The GNN is trained to generate atomic embeddings that encapsulate both the local and global chemical environments of each atom, which is crucial for

accurate chemical shift predictions. The atomic embeddings are combined with the solvent embedding produced by the solvent encode, which allows our model to learn the influence of solvent on

chemical shifts. The combined embeddings are mapped by the Multi-Layer Perceptron (MLP) modules to HSQC chemical shifts. Our framework employs a two-stage transductive strategy to train the

model while addressing the aforementioned challenges. In the first stage, we use a large amount of annotated 1D NMR data to pre-train the model via Multi-Task learning. This enables the

model to adeptly grasp the intricate relationship between atomic interactions and NMR signals, laying a robust foundation for the subsequent stage. Next, the model is refined on a set of

unlabeled HSQC spectra via Iterative Unsupervised Learning, enhancing the model’s capability in predicting and interpreting HSQC spectra. Our final model achieves MAEs of 0.165 ppm and 2.05

ppm for 1H and 13C shifts respectively, while accurately assigning cross peaks. It demonstrates a consistent performance across various molecular weight and saccharide categories,

significantly outperforming the traditional methods, and shows convincing generalization capabilities to less represented samples from the training dataset. In the future, we plan to refine

our model by developing 3D-GNN models that are able to consider 3D structural information such as spatial orientation and conformational flexibility. This enhancement should enable us to

handle other 2D NMR spectra, such as Correlation Spectroscopy and Nuclear Overhauser Effect Spectroscopy, thus broadening its applicability and making a more substantial contribution to the

field of chemical analysis. METHODS In this section, we explain the components of our model and the training strategy in detail. DATA The pre-training dataset used in the MTT process is a 1D

NMR dataset from NMRShiftDB29, which contains  ~24,000 annotated NMR spectra collected from 22,663 distinct molecules. The datasets used in the unsupervised transfer learning process

consist of a training dataset containing  ~19,000 experimental HSQC spectra and a validation dataset containing  ~5000 HSQC spectra, collected from HMDB25 and CH-NMR-NP26. All data was

accessed in September 2023, with no evidence of potential bias. To prevent data leakage in the validation dataset, duplicated spectra and molecules were removed. RDKit package in Python is

used to perform sanity check for all SMILES strings to generate valid molecular topology graph. To quantitatively evaluate our model, we built a test dataset by randomly selecting 500

spectra and manually annotating them to establish the ground truth (see Section “Performance on HSQC cross peak prediction and assignment” for the annotation process). Additionally, to

compare our model with two conventional tools (ChenDraw and Mestrenova) in chemistry, we randomly selected several molecules from this test dataset, consisting  ~150 cross-peaks. Since it is

labor-intensive to derive HSQC shifts from molecular formulas using these established tools, stratified sampling was used to select these samples, ensuring the coverage of different

molecular weight groups (0–499 Dalton, 500–999 Dalton, and 1000+ Dalton). The comparison results are presented in Section “Comparison with traditional tools”. 2D NMR PREDICTION MODEL As

illustrated in Fig. 1A, our model contains a GNN component for encoding molecular features and a solvent encoder component for embedding solvent information. The GNN component learns atomic

embeddings that capture both the local and global chemical environments of each atom, which are essential for understanding the observed NMR chemical shifts. The learnt atom representations

are expanded by the solvent embedding, and then are mapped to 13C and 1H cross peaks by a MLP component. GNN A molecule can be represented by a graph _G_ = (_V_, _E_), where _V_ is the node

set representing atoms and _E_ is the edge set representing chemical bonds. Three features are provided for each node: atomic type, chirality, and hybridization. Also, two features are

considered for each edge: bond type and bond direction. Bond types include Single, Double, Triple, and Aromatic, each reflecting a distinct configuration of electron sharing between atoms.

Bond direction includes None, EndUpRight, and EndDownRight, primarily representing stereochemistry in double bonds. Each atom’s feature vector is embedded into a representation vector by a

learnable encoder. Similarly, each edge’s feature vector is embedded into a representation vector of the same length by another learnable encoder. Then, a GNN model36,37,38,39,40 utilizes

the message passing mechanism to iteratively refine the representation of each node based on information from its neighbors and connected edges. This mechanism allows the learnt node

representation to effectively capture structural context, reflecting the foundational principles of atomic interactions. Our implementation of the message passing mechanism is illustrated in

Fig. 7. It iterates for a predefined number of layers _L_, facilitating the propagation of information throughout the graph. Consequently, each node can gradually accumulate information

from a wider neighborhood across successive layers. This allow the final representation of each node to capture both local and global structural information. Our model features 5 GNN layers,

with an atomic embedding dimension of 512. SOLVENT ENCODER Since the solvent has a profound impact on NMR chemical shifts, we incorporated a trainable solvent encoder component into our

model to accurately capture this influence. We identified the following 9 principal solvent groups based on their prevalence in our dataset and domain-specific understandings of their

distinct impacts on NMR shifts. These groups include trichloromethane, dimethyl sulfoxide, acetone, acids, benzene, methanol, pyridine, water, and an additional category to encompass any

unspecified solvents from our dataset (termed “unknown”). The solvent encoder transforms each discrete solvent group _i_ into a unique, dense feature vector \({S}_{i}^{d}\), where _d_ is the

embedding dimension. These learnable vectors are optimized alongside other model parameters during training, resulting in representations that accurately reflect the impact of each solvent

class. Given the different sensitivities of carbon (C) and hydrogen (H) nuclei to solvent environments, different embedding dimensions _d_ can be chosen to tailor the solvent effect modeling

for each nuclei type. A larger embedding dimension _d_ allows the embedding to more effectively capturing the nuanced influence of solvents on NMR shifts. In our implementation, the solvent

embedding dimension for hydrogen (H) is set to 32. ATOMIC NMR SHIFT PREDICTION Finally, the embedding of each atom \({h}_{v}^{(L)}\) and the solvent embedding \({S}_{i}^{d}\) for each

solvent class _i_ are concatenated to produce a holistic representation of the atom within the context of its molecular structure and the given solvent. This combined representation is

subsequently processed by a MLP network to predict the NMR shifts for the atom: $${y}_{v}=\,{\mbox{MLP}}\,({{{\bf{h}}}}_{v}^{(L)}\oplus {{{\bf{S}}}}_{i}^{d})$$ (1) where _y__v_ is the

predicted chemical shift of atom _v_, \({h}_{v}^{(L)}\) is the atom level embedding produced by GNN, _S__d_ is the solvent embedding, and ⊕ is the concatenation operation. By integrating

solvent embedding and atomic embedding, the model effectively combines intrinsic molecular properties and solvent effects, enhancing its ability to predict atomic NMR shifts accurately. Two

separate MLP modules are used for predicting 13C and 1H shift in the cross peak predictions, respectively. Each C atom can bond up to 4 H atoms. When bonded to one, three, or four H atoms, a

C atom typically shows only one cross peak in an experimental spectrum. However, when a C atom is connected to two H atoms, up to two cross peaks may be observed, depending on the chiral

center. Consequently, a C atom can exhibit at most two 13C and 1H cross peaks. In light of this observation, one MLP module is dedicated to predicting the 13C shifts and another MLP module

for the corresponding 1H shifts. For cross peak predictions, the 13C shifts are predicted using the embeddings of C atoms. The corresponding 1H shift predictions for each C atom incorporate

aggregates of embeddings from all bonded H atoms, resulting in two predictions that are typically very similar when only one cross peak is theoretically possible. This design enhances the

model’s accuracy in predicting 1H shifts by leveraging the C atom-centered aggregation of the H atom context. By integrating the contextual dynamics around each C atom, the model provides a

more detailed and accurate mapping of hydrogen environments, crucial for pinpointing precise cross peaks in complex HSQC spectra. In our implementation, we used 2 MLP layers, with the hidden

dimensions to be 128 and 64 respectively. The dropout mechanism, which randomly deactivates a subset of neurons during the forward pass, is employed during training to prevent overfitting.

By reducing the model’s dependence on specific neurons, dropout encourages the model to learn more robust and generalized patterns. During inference, dropout is typically disabled to ensure

deterministic predictions. However, when enabled during inference, dropout can be leveraged to estimate uncertainty by calculating the standard deviation across multiple predictions18. An

example of this uncertainty estimation is provided in Supplementary Information, Section 4, Supplementary Table 1. TRAINING STRATEGY The cross peaks are notably sparse in an HSQC spectrum,

where typical resolutions for 13C and 1H shifts are 0.1 and 0.01 ppm, respectively. A typical HSQC spectrum can include 20,000 readings, covering 13C shifts from 0 to 200 ppm and 1H shifts

from 0 to 10 ppm. However, almost all of these readings are zeros, with only a small fraction representing the potential cross peaks of C–H bonds, crucial for molecular structure analysis.

Moreover, the scarcity of annotated HSQC data, particularly the labor-intensive annotations that link cross peaks to C–H bonds, makes model training difficult. To deal with this issue, we

deployed MTT to pre-train the model using an extensive annotated 1D NMR dataset (Fig. 1B). This step acclimates the model with a broad range of molecular structures and their chemical

shifts, and enables it to capture the intricate interplay between molecular structures and their NMR characteristics. Subsequently, we utilize an unsupervised strategy to refine the model

iteratively on the HSQC dataset (Fig. 1C). Through iterative cycles of prediction, annotation, and re-training, the model progressively enhances its understanding of the complex

relationships and patterns within the HSQC spectra, thus improving its predictive accuracy and providing precise cross peak alignments. By combining the MTT and unsupervised transfer

learning, we extend our annotation capabilities from 1D to 2D data, thereby enhancing the model’s predictive power and utility as a robust tool for NMR spectra analysis. PRE-TRAINING ON 1D

NMR DATA In the pre-training phase, we utilized approximately 24,000 annotated 1D NMR data points. Among these, around 22,000 samples exclusively feature 13C shifts, approximately 400

samples solely exhibit 1H shifts, while roughly 1600 samples contain both 1H and 13C shifts. To train the model effectively for predicting both 1H and 13C shifts, we adapt the MTT approach,

which enables simultaneous training on multiple related tasks. When the input data contains 13C shifts, the model predicts only carbon shifts and assesses the errors between the predicted

and actual values. Conversely, when the data sample contains 1H shifts, the hydrogen shift prediction module is activated. In both scenarios, the embeddings of 13C and 1H atoms in the GNN

module are updated simultaneously, benefiting from the message passing mechanism. Therefore, the learnt representations implicitly contain a basic understanding of C–H relationships,

essential for the interpretation of HSQC data. However, the relative scarcity of 1H shift data, due to the difficulties in accurately obtaining and extracting peaks 1H from experimental

data, complicates the training process as focusing extensively on one type of shift could compromise the model’s ability to accurately predict the other. To handle this problem in the MTT

training, we performed over-sampling on a subset of data that contain both 1H and 13C shifts, and those containing only 1H shifts. Consequently, the learned representations develop a

fundamental understanding of C–H relationships, crucial for interpreting HSQC data effectively. This integration of learned atomic relationships streamlines the transition to HSQC cross peak

predictions, thereby enhancing the model’s accuracy and efficiency in analyzing HSQC spectra. UNSUPERVISED FINE-TUNING ON HSQC DATA The model pre-trained on the 1D NMR dataset has limited

ability to predict HSQC cross-peaks from molecular structures due to the differences in data pre-processing and data distribution. First, in the 1D NMR data from NMRShiftDB2, the chemical

shifts of non-singlet peaks are averaged as ground truth. For example, whether the group is methine (-CH), methylene (-CH2), or methyl (-CH3), the proton shifts may be averaged into a single

value. In contrast, HSQC data captures C-H bonds and typically displays two cross-peaks for prochiral methylene groups due to the different environments of the two hydrogens. Additionally,

the proton chemical shifts of HSQC or HMQC cross peaks represent 13C-bound protons, whereas the signals in the 1H mainly represent 12C-bound protons, potentially leading to subtle

differences in chemical shift values41. Second, the molecule distributions in our 1D NMR data and HSQC data exhibit significant differences (see Supplementary Information, Section 3,

Supplementary Fig. 10, for data distribution plots). The HSQC dataset comprises 76.34% small molecules and 90.33% non-saccharides, whereas the 1D NMR dataset contains 98.80% small molecules

and 99.95% non-saccharides. Lastly, solvent information is not available in 1D NMR dataset, and is recorded as “unknown” in the modeling framework, whereas most molecules in the HSQC dataset

are associated with known solvent environments. This makes the fine-tuning step essential for the success of our solvent-aware framework. However, the HSQC dataset is not annotated. In

response, we implement an unsupervised training strategy (Fig. 1C), which iterates between (a) aligning cross peak prediction from the model with the experiment observations to annotate the

HSQC data and (b) using the newly acquired annotations to fine-tune the NMR prediction model, until convergence. PSEUDO-ANNOTATION OF HSQC At the end of each round in the unsupervised

learning process, the model’s predicted signals are aligned with the experimental observations to create pseudo-labels. In straightforward cases where the number of C–H bonds in a molecular

graph matches the observed HSQC cross peaks, the Hungarian algorithm42,43 is used. This classic optimization technique solves assignment problems by minimizing the cost of matching a set of

predictions to a set of observations. In the context of NMR analysis, the “cost” is defined as the discrepancy between the predicted chemical shifts and the actual shifts observed

experimentally. By systematically reducing these differences, the Hungarian algorithm achieves an optimal one-to-one correspondence between predicted shift pairs and experimental signals,

even in complex scenarios with potential signal overlap. However, in most cases, the number of C–H bonds within a molecule exceeds the number of signals recorded, making peak alignment more

difficult. This mismatch in numbers arises from several factors: firstly, rotational equivalence can reduce the number of signals, with a single peak representing all three C–H bonds for

methyl groups; secondly, symmetrical molecular structures can result in a single detectable signal for multiple symmetric C–H bonds, as seen in benzene molecule where only one peak

represents all six C–H bonds; lastly, in highly complex molecules, overlapping signals obscure some peaks, reducing the detectability of individual C–H bonds from experiments. To overcome

this issue, we utilize the graduated assignment algorithm16,44, which facilitates matching between graphs of different node counts, making it particularly suitable for this scenario. In this

algorithm, our model’s predicted C–H shifts \({({C}^{i},{H}^{i})}_{i = 0}^{N}\) and the observed C–H signals \({({C}^{j},{H}^{j})}_{j = 0}^{M}\) of each molecule are conceptualized as

points on a 2D plane, where _N_ and _M_ are numbers of predicted and observed C–H shifts respectively. These points are then treated as vertices in two fully connected graphs, _G_1 for

predicted shifts and _G_2 for observed signals. The similarity between nodes is defined as the inverse of differences between predicted chemical shifts (node in _G_1) and observed shifts

(node in _G_2). Specifically, for each predicted shift, we compute its difference with every observed shift, where a smaller difference indicates a higher similarity. The derive the

assignment matrix _A_ where each element _A__u__v_ ∈ {0, 1} indicates whether node _u_ in _G_1 matches with node _v_ in _G_2, the algorithm first finds the soft matching matrix that relaxes

the binary constraint _A__u__v_ ∈ {0, 1} to a continuous range [0, 1], then converts it into hard assignment in a greedy way, enabling one-to-many matching. DATA AVAILABILITY HSQC data used

for model performance testing is available here(via Google Drive), and the training and validation datasets will be available upon request. CODE AVAILABILITY The code is available in Github:

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references ACKNOWLEDGEMENTS This work was supported by GlycoMIP, a National Science Foundation (NSF) Materials Innovation Platform funded through Cooperative Agreement DMR-1933525, NSF OAC

1920147, as well as NIH R24GM137782. AUTHOR INFORMATION Author notes * These authors contributed equally: Yunrui Li, Hao Xu. AUTHORS AND AFFILIATIONS * Department of Computer Science,

Brandeis University, Waltham, MA, USA Yunrui Li & Pengyu Hong * Department of Medicine, Harvard Medical School, Boston, MA, USA Hao Xu * Complex Carbohydrate Research Center, University

of Georgia, Athens, GA, USA Ambrish Kumar, Christian Heiss & Parastoo Azadi * Department of Chemistry, Boston College, Chestnut Hill, MA, USA Duo-Sheng Wang Authors * Yunrui Li View

author publications You can also search for this author inPubMed Google Scholar * Hao Xu View author publications You can also search for this author inPubMed Google Scholar * Ambrish Kumar

View author publications You can also search for this author inPubMed Google Scholar * Duo-Sheng Wang View author publications You can also search for this author inPubMed Google Scholar *

Christian Heiss View author publications You can also search for this author inPubMed Google Scholar * Parastoo Azadi View author publications You can also search for this author inPubMed 

Google Scholar * Pengyu Hong View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS Y. Li and H. Xu: idea generation, algorithm design, code

implementation, data analysis, manuscript writing, editing, and revision. A. Kumar and D. Wang: data annotation. C. Heiss and P. Azadi: supervision. P. Hong: supervision, research planning,

funding acquisition, manuscript review, editing and revision. All authors reviewed the manuscript. H. Xu’s work was done while he was at Brandeis University. CORRESPONDING AUTHOR

Correspondence to Pengyu Hong. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. PEER REVIEW PEER REVIEW INFORMATION _Communications Chemistry_ thanks the

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