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Applications · Chemistry, Physics, and Earth Sciences

Sungwon Park, Anthony Zhou, Hongjoong Kim, Amir Barati Farimani

Neural operators have emerged as a powerful paradigm for learning discretization-invariant function-to-function mappings in scientific computing. However, many practical systems are inherently stochastic, making principled uncertainty quantification essential for reliable deployment. To address this, we introduce a simple add-on, the *diffusion last layer* (DLL), a lightweight probabilistic head that can be attached to arbitrary neural operator backbones to model predictive uncertainty. Motivated by the relative smoothness and low-dimensional structure often exhibited by PDE solution distributions, DLL parameterizes the conditional output distribution directly in function space through a low-rank Karhunen-Loève expansion, enabling efficient and expressive uncertainty modeling. Across stochastic PDE operator learning benchmarks, DLL improves generalization and uncertainty-aware prediction. Moreover, even in deterministic long-horizon rollout settings, DLL enhances rollout stability and provides meaningful estimates of epistemic uncertainty for backbone neural operators.

Applications · Chemistry, Physics, and Earth Sciences

Xinyu Wang, Ruoyu Wang, Qiangwei Peng, Peijie Zhou, Tiejun Li

Reconstructing dynamical evolution from limited observations is a fundamental challenge in single-cell biology, where dynamic unbalanced optimal transport (OT) provides a principled framework for modeling coupled transport and mass variation. However, existing approaches rely on trajectory simulation at inference time, making inference a key bottleneck for scalable applications. In this work, we propose a mean-flow framework for unbalanced flow matching that summarizes both transport and mass-growth dynamics over arbitrary time intervals using mean velocity and mass-growth fields, enabling fast one-step generation without trajectory simulation. To solve dynamic unbalanced OT under the Wasserstein-Fisher-Rao geometry, we further build on this framework to develop **Wasserstein-Fisher-Rao Mean Flow Matching (WFR-MFM)**. Across synthetic and real single-cell RNA sequencing datasets, WFR-MFM achieves orders-of-magnitude faster inference than a range of existing baselines while maintaining high predictive accuracy, and enables efficient perturbation response prediction on large synthetic datasets with thousands of conditions.

Applications · Chemistry, Physics, and Earth Sciences

Lisa Schneckenreiter, Sohvi Luukkonen, Lukas Friedrich, Daniel Kuhn, Günter Klambauer

Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce **Con**trastive **G**eometric **L**earning for **U**nified Computational **D**rug D**e**sign (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for pre-defined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

Applications · Chemistry, Physics, and Earth Sciences

Chenguang Wang, Zihan Zhou, LEI BAI, Tianshu Yu

Template-free retrosynthesis methods treat the task as black-box sequence generation, limiting learning efficiency, while semi-template approaches rely on rigid reaction libraries that constrain generalization. We address this gap with a key insight: atom ordering in neural representations matters. Building on this insight, we propose a structure-aware template-free framework that encodes the two-stage nature of chemical reactions as a positional inductive bias. By placing reaction center atoms at the sequence head, our method transforms implicit chemical knowledge into explicit positional patterns that the model can readily capture. The proposed RetroDiT backbone, a graph transformer with rotary position embeddings, exploits this ordering to prioritize chemically critical regions. Combined with discrete flow matching, our approach decouples training from sampling and enables generation in 20--50 steps versus 500 for prior diffusion methods. Our method achieves state-of-the-art performance on both USPTO-50k (61.2\% top-1) and the large-scale USPTO-Full (51.3\% top-1) with predicted reaction centers. With oracle centers, performance reaches 71.1\% and 63.4\% respectively, surpassing foundation models trained on 10 billion reactions while using orders of magnitude less data. Ablation studies further reveal that structural priors outperform brute-force scaling: a 280K-parameter model with proper ordering matches a 65M-parameter model without it.

Applications · Chemistry, Physics, and Earth Sciences

Lin Huang, Chengxiang Huang, Ziang Wang, Yiyue Du, Chu Wang, Haocheng Lu, Yunyang Li, Xiaoli LIU, Arthur JIANG, Jia Zhang

Equivariant Graph Neural Networks (EGNNs) have become a widely used approach for modeling 3D atomistic systems. However, mainstream architectures face critical scalability bottlenecks due to the explicit construction of geometric features or dense tensor products on \textit{every} edge. To overcome this, we introduce \textbf{E2Former-V2}, a scalable architecture that integrates algebraic sparsity with hardware-aware execution. We introduce \textbf{Equivariant Axis-Aligned Sparsification (EAAS)}, which leverages an $\mathrm{SO}(3)\!\rightarrow\!\mathrm{SO}(2)$ change of basis to convert dense Wigner-$6j$ tensor contractions into sparse, parity-based re-indexing operations. Building on this representation, we propose \textbf{On-the-Fly Equivariant Attention}, a fully node-centric mechanism implemented via a fused Triton kernel. By eliminating materialized edge tensors and maximizing SRAM utilization, our kernel achieves up to \textbf{20$\times$ higher TFLOPS} than standard implementations. Experiments on SPICE and OMol25 show that E2Former-V2 preserves predictive accuracy while substantially accelerating inference, demonstrating the practical feasibility of large equivariant transformers on commodity GPUs.

Applications · Chemistry, Physics, and Earth Sciences

Paul Garnier, Vincent Lannelongue, Elie Hachem

Machine Learning surrogates for Computational Fluid Dynamics (CFD), particularly Graph Neural Networks (GNNs) and Transformers, have become a new important approach for accelerating physics simulations. However, we identify a critical bottleneck in the field: while architectures have advanced significantly, the underlying training paradigms remain bound to naive assumptions, such as node-wise supervision and explicit Euler time-stepping. These legacy choices ignore the stiff dynamics and local flux continuity inherent to numerous partial differential equations resolution methods, such as Finite Element, Difference, or Volume (FEM). In this work, we propose a unified framework to bridge the gap between geometric deep learning and rigorous numerical analysis. We introduce three key innovations: (1) Multi Node Prediction, a novel objective that predicts field values for a node's full local topology, enforcing spatial derivative consistency; (2) Temporal Correction, replacing unstable explicit schemes with a predictor–corrector via temporal Cross-Attention; and (3) Geometric Inductive Biases, leveraging 3D Rotary Positional Embeddings (RoPE) to robustly capture rotational symmetries in unstructured meshes. We evaluate this framework across three architectures (MeshGraphNet, Transolver, and a Transformer) on diverse physics datasets. Our approach yields consistent improvements in accuracy and stability, particularly in long-horizon rollouts, while producing latent representations that generalize to unseen subtasks such as Wall Shear Stress or Pressure prediction.

Applications · Chemistry, Physics, and Earth Sciences

Zenong Li, Wei Xian Lim, Wai Lee Chan, Adams Wai Kin Kong

To overcome computation burden of traditional computational fluid dynamics (CFD) simulations, researchers have explored different architectures to develop physics-informed simulation methods. Among them, graph neural networks (GNN) are most suitable for adopting CFD meshes, which are extensively used in engineering and industrial applications. However, classical GNNs propagate information among neighbour nodes, which highly restrict information exchange within the network. To address this issue, graph rewiring methods have been developed for generic graph problems, but not particular for fluid simulation. PIORF, introducing edges connecting distant nodes, is the first graph rewiring method to do so, and previous experiments have demonstrated its effectiveness against state-of-the-art generic rewiring methods. Nevertheless, in this work, we found that simply connecting all 2-hop nodes can provide competitive performance with PIORF. This result raises three questions: 1) Is physics-informed rewiring really useful for improving flow predictions? 2) Should we consider just local connection, instead of connecting distant nodes? 3) Do we need to change the connections based on input flow for rollout simulations? By thoroughly adopting physical fluid principles, we propose a simple yet very efficient method, Flow Alignment Rewiring (FLARE) technique, which connects 2-hop nodes only when the node direction aligns with input flow direction. Hence, FLARE is a physics-informed local rewiring method, different from PIORF and well-aligned with fluid physics. Extensive numerical experiments on flows over a cylinder and single and tandem airfoil under different flow conditions and deep network architectures demonstrate that FLARE outperforms PIORF and various 2-hop rewiring approaches by a significant margin.

Applications · Chemistry, Physics, and Earth Sciences

Zhixiang Cheng, Hongxin Xiang, Mingquan Liu, Tengfei Ma, Yingzhuo Tu, Wenjie Du, Bosheng Song, Yiping Liu, xiangxiang Zeng

Precise property prediction of organic materials is pivotal for next-generation electronic and energy devices. In density functional theory (DFT), the electron density (ED) serves as the fundamental determinant of material properties. Yet, establishing it as an input modality for material property prediction has been impeded by two practical barriers: scarce large-scale ED data and the enormous computational complexity of ED representation. To bridge these gaps, we introduce VisionED, an efficient physics-informed model pre-trained on electron-density images. We curate a dataset of 2 million molecules and represent ED as multi-shot images that efficiently encode both geometric and electronic structure. VisionED is then pre-trained on 12 million multi-shot ED images via cross-scale, physics-informed pretext tasks. Empirical evaluations on photovoltaic and organic chromophore datasets show that VisionED outperforms state-of-the-art baselines by up to 27.0\%, exhibiting superior robustness under distribution shifts and data scarcity. Notably, the model generalizes to unseen device-scale applications, successfully recovering experimental trends and mixing-ratio effects in ternary blends with an average accuracy of 93\%. Moreover, relative to the previous ED point cloud, the ED image improves performance by 26.2\% with 2.6$\times$ fewer memory and 4.6$\times$ lower time. The code and data are available at https://anonymous.4open.science/r/VisionED-AC1B.

Applications · Chemistry, Physics, and Earth Sciences

Francisco Giral, Álvaro Sevillano, Ignacio Perez, Ricardo Vinuesa, Soledad Le Clainche

Urban wind flow reconstruction is essential for assessing air quality, heat dispersion, and pedestrian comfort, yet remains challenging when only sparse sensor data are available. We propose GenDA, a generative data assimilation framework that reconstructs high-resolution wind fields on unstructured meshes from limited observations. The model employs a multiscale graph-based diffusion architecture trained on computational fluid dynamics (CFD) simulations and interprets classifier-free guidance as a learned posterior reconstruction mechanism: the unconditional branch learns a geometry-aware flow prior, while the sensor-conditioned branch injects observational constraints during sampling. This formulation enables obstacle-aware reconstruction and generalization across unseen geometries, wind directions, and mesh resolutions without retraining. We consider both sparse fixed sensors and trajectory-based observations using the same reconstruction procedure. When evaluated against supervised graph neural network (GNN) baselines and classical reduced-order data assimilation methods, GenDA reduces the relative root-mean-square error (RRMSE) by 25-57% and increases the structural similarity index (SSIM) by 23-33% across the tested meshes. Experiments are conducted on Reynolds-averaged Navier-Stokes (RANS) simulations of a real urban neighborhood in Bristol, United Kingdom, at a characteristic Reynolds number of $\mathrm{Re}\approx2\times10^{7}$, featuring complex building geometry and irregular terrain. The proposed framework provides a scalable path toward generative, geometry-aware data assimilation for environmental monitoring in complex domains.

Applications · Chemistry, Physics, and Earth Sciences

Lixing Zhang, Guijing Duan, Di Luo

We present a comprehensive benchmarking dataset and empirical scaling-law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many-body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural-network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establish a unified dataset-driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.

Applications · Chemistry, Physics, and Earth Sciences

Aleksander Krasowski, Jonas Naujoks, Moritz Weckbecker, Galip Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen

Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability. To address this issue, we introduce PINNfluence, a training data attribution framework for interpreting PINNs based on influence functions. By extending influence functions to composite physics-informed training objectives, we enable fine-grained attribution between predictions, loss components, and training data points. Through benchmark experiments across various PDEs, we demonstrate that influence patterns provide granular diagnostics that distinguish different PINN failure modes. PINNfluence thus opens a new avenue for understanding and improving the reliability of PINNs through the lens of their data.

Applications · Chemistry, Physics, and Earth Sciences

In Huh, Changwook Jeong, Muhammad Alam

Data-driven dynamical system models often fail to recover the long-term structure of the underlying system, as their behavior is weakly constrained off the data manifold. Conjugacy-based approaches address this limitation by learning a diffeomorphism that pushes forward a source vector field to match observed dynamics, inheriting qualitative topology from the source. However, such methods typically presuppose that the chosen source system is topologically compatible with the target data. When this assumption is violated, the conjugacy problem becomes ill-posed, and arbitrary corrections can be traded off against diffeomorphic variation, leading to non-identifiability. We propose a framework that relaxes this assumed prior by jointly learning the diffeomorphic conjugacy together with controlled adjustments to the source dynamics via low-dimensional context modulation. Inspired by versal unfolding theory, we enforce the modulation space to be orthogonal to the worst-case orbit-tangent directions, obtained by adversarially searching over a class of parameterized diffeomorphisms. This promotes an identifiable decomposition of dynamical variation into diffeomorphic and intrinsic, topology-changing components, enabling interpretable corrections that recover the canonical structure such as normal forms and symmetries.

Applications · Chemistry, Physics, and Earth Sciences

Shizheng Wen, Mingyuan chi, Tianwei Yu, Ben Moseley, Mike Yan Michelis, Pu Ren, Hao Sun, Siddhartha Mishra

We present a unified algorithmic framework for the numerical solution, constrained optimization, and physics-informed learning of PDEs with a variational structure. Our framework is based on a Galerkin discretization of the underlying variational forms, and its high efficiency stems from a novel highly-optimized and GPU-compliant TensorGalerkin framework for linear system assembly (stiffness matrices and load vectors). TensorGalerkin operates by tensorizing element-wise operations within a Python-level Map stage and then performs global reduction with a sparse matrix multiplication that performs message passing on the mesh-induced sparsity graph. It can be seamlessly employed downstream as i) a highly-efficient numerical PDEs solver, ii) an end-to-end differentiable framework for PDE-constrained optimization, and iii) a physics-informed operator learning algorithm for PDEs. With multiple benchmarks, including 2D and 3D elliptic, parabolic, and hyperbolic PDEs on unstructured meshes, we demonstrate that the proposed framework provides significant computational efficiency and accuracy gains over a variety of baselines in all the targeted downstream applications.

Applications · Chemistry, Physics, and Earth Sciences

Seongsu Kim, Chanhui Lee, Yoonho Kim, Seongjun Yun, Honghui Kim, Nayoung Kim, Changyoung Park, Sehui Han, Sungbin Lim, Sungsoo Ahn

Recently, machine learning Hamiltonian (MLH) models have gained traction as fast approximations of electronic structures such as orbitals and electron densities, while also enabling direct evaluation of energies and forces from their predictions. However, despite their physical grounding, existing Hamiltonian models are evaluated mainly by reconstruction metrics, leaving it unclear how well they perform as energy–force predictors. We address this gap with a benchmark that computes energies and forces directly from predicted Hamiltonians. Within this framework, we propose QHFlow2, a state-of-the-art Hamiltonian model with an SO(2)-equivariant backbone and a two-stage edge update. QHFlow2 achieves $40\%$ lower Hamiltonian error than the previous best model with fewer parameters. Under direct evaluation on MD17/rMD17, it is the first Hamiltonian model to reach NequIP-level force accuracy while achieving up to $20\times$ lower energy MAE. On QH9, QHFlow2 reduces energy error by up to $20\times$ compared to MACE. Finally, we demonstrate that QHFlow2 exhibits consistent scaling behavior with respect to model capacity and data, and that improvements in Hamiltonian accuracy effectively translate into more accurate energy and force computations.

Applications · Chemistry, Physics, and Earth Sciences

Ziyang Yu, Yi He, Wenbing Huang, Wen Yan, Yang Liu

Estimating free energy differences quantifies thermodynamic preferences in molecular interactions, which is central to chemistry and drug discovery. Despite fruitful progress, existing methods still face key limitations: classical computational approaches remain prohibitively expensive due to their reliance on extensive molecular dynamics simulations, while deep learning-based methods are constrained by either less-expressive generative models or input dimensions tied to a specific system, resulting in negligible generalization. To address these challenges, we propose CARD, a generative framework that employs a novel radix-based decomposition to bijectively convert 3D coordinates into mixed discrete-continuous sequences, enabling coarse-to-fine autoregressive modeling with enhanced expressiveness. Notably, the model corresponds to a distribution with zero free energy, serving as a proposal for absolute free energy computation of arbitrary systems without relying on alchemical pathways. Experiments across diverse tasks demonstrate that CARD matches the accuracy of classical computational methods on unseen systems with diverse topologies, while achieving an approximately 40-fold speedup in inference.

Applications · Chemistry, Physics, and Earth Sciences

Jules Berman, Tobias Blickhan, Benjamin Peherstorfer

In existing works on population dynamics inference, there is a focus on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamic, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize with general vector fields as well as choose other selection criteria beyond minimal energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.

Applications · Chemistry, Physics, and Earth Sciences

Xinyi Li, Sai Wang, Yutian Lin, Yu Wu

Retrosynthesis prediction aims to infer the reactant molecule based on a given product molecule, which is a fundamental task in chemical synthesis. However, existing models rely on static pattern-matching paradigm, which limits their ability to perform effective logic decision-making, leading to a black-box process. Building on this, we propose Retro-Expert, an interpretable retrosynthesis framework that performs collaborative reasoning by combining the complementary reasoning strengths of Large Language Models and specialized models via reinforcement learning. It outputs natural language explanations grounded in chemical logic through three components: (1) specialized models analyze the product to construct high-quality chemical decision space, (2) LLM-driven critical reasoning to generate predictions and corresponding interpretable reasoning path, and (3) reinforcement learning optimizing interpretable decision policy. Experiments show that Retro-Expert not only surpasses both LLM-based and specialized models across different metrics but also provides expert-aligned explanations that bridge the gap between AI predictions and actionable chemical insights.

Applications · Chemistry, Physics, and Earth Sciences

Riccardo Tedoldi, Ola Engkvist, Patrick Bryant, Hossein Azizpour, Jon Paul Janet, Alessandro Tibo

Sampling useful three-dimensional molecular structures along with their most favorable conformations is a key challenge in drug discovery. Current state-of-the-art 3D de-novo design flow matching or diffusion-based models are limited to generating a single conformation. However, the conformational landscape of a molecule determines its observable properties and how tightly it is able to bind to a given protein target. By generating a representative set of low-energy conformers, we can more directly assess these properties and potentially improve the ability to generate molecules with desired thermodynamic observables. Towards this aim, we propose \textit{FlexiFlow}, a novel architecture that extends flow-matching models, allowing for the joint sampling of molecules along with multiple conformations while preserving both equivariance and permutation invariance. We demonstrate the effectiveness of our approach on the QM9 and GEOM Drugs datasets, achieving state-of-the-art results in molecular generation tasks. Our results show that FlexiFlow can generate valid, unstrained, unique, and novel molecules with high fidelity to the training data distribution, while also capturing the conformational diversity of molecules. Moreover, we show that our model can generate conformational ensembles that provide similar coverage to state-of-the-art physics-based methods at a fraction of the inference time. Finally, FlexiFlow can be successfully transferred to the protein-conditioned ligand generation task, even when the dataset contains only static pockets without accompanying conformations.

Applications · Chemistry, Physics, and Earth Sciences

Wenjie Luo, chaorong li, Chuanhu Deng, Zhuo Wang

Reliable long-horizon precipitation nowcasting requires preserving fine-scale echo structures while maintaining coherent transport. Although Rectified Flow (RF) can generate detail-preserving future sequences, numerical ODE integration compounds velocity estimation errors and induces progressive off-manifold drift, causing morphological distortions at extended lead times. We propose Physically-guided Data-space Rectified Flow (PDRF), which re-parameterizes the generative ODE in data space: the network predicts the clean future sequence, analytically inducing a coupled vector field with an implicit restoring effect that suppresses drift. We also introduce a soft Semi-Lagrangian teacher based on an advection prior to regularize large-scale transport, while allowing local growth/decay/deformation to be learned from data. Experiments on four public benchmarks demonstrate consistent improvements in event-based skill and better preservation of intense-echo morphology over long horizons.

Applications · Chemistry, Physics, and Earth Sciences

Bogdan Zagribelnyy, Ivan Ilin, Maksim Kuznetsov, Nikita Bondarev, Roman Schutski, Thomas MacDougall, Rim Shayakhmetov, Zulfat Miftahutdinov, Mikolaj Mizera, Vladimir Aladinskiy 等

Recent progress has expanded the use of large language models (LLMs) in drug discovery, including synthesis planning. However, objective evaluation of retrosynthesis performance remains limited. Existing benchmarks and metrics typically rely on published synthetic procedures and Top-K accuracy based on single ground-truth, which does not capture the open-ended nature of real-world synthesis planning. We propose a new benchmarking framework for single-step retrosynthesis that evaluates both general-purpose and chemistry-specialized LLMs using ChemCensor, a novel metric for chemical plausibility. By emphasizing plausibility over exact match, this approach better aligns with human synthesis planning practices. We also introduce CREED, a novel dataset comprising millions of ChemCensor-validated reaction records for LLM training, and use it to train a model that improves over the LLM baselines under this benchmark.