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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.

Deep Learning · Algorithms

Cédric Goemaere, Gaspard Oliviers, Rafal Bogacz, Thomas Demeester

Predictive Coding (PC) offers a brain-inspired alternative to backpropagation for neural network training, described as a physical system minimizing its internal energy. However, in practice, PC is predominantly digitally simulated, requiring excessive amounts of compute while struggling to scale to deeper architectures. This paper reformulates PC to overcome this hardware-algorithm mismatch. First, we uncover how the canonical state-based formulation of PC (sPC) is, by design, deeply inefficient in digital simulation, inevitably resulting in exponential signal decay that stalls the entire minimization process. Then, to overcome this fundamental limitation, we introduce error-based PC (ePC), a novel reparameterization of PC which does not suffer from signal decay. Though no longer biologically plausible, ePC numerically computes exact PC weights gradients and runs orders of magnitude faster than sPC. Experiments across multiple architectures and datasets demonstrate that ePC matches backpropagation's performance even for deeper models where sPC struggles. Besides practical improvements, our work provides theoretical insight into PC dynamics and establishes a foundation for scaling PC-based learning to deeper architectures on digital hardware and beyond.

Probabilistic Methods · Gaussian Processes

Hui Li, Huafeng Liu, Chenguang Li, Tianxiao Zhang, Yajun Yang, Liping Jing

Parametric partial differential equations (PDEs) serve as fundamental models across science and engineering, yet constructing fast and accurate surrogate models from sparse, irregularly sampled observations with reliable uncertainty quantification remains challenging. Existing approaches struggle to simultaneously handle variable observation patterns, preserve physics consistency, and provide well-calibrated predictive uncertainty. We introduce Bias-Spectrum Neural Processes (BSNP), a unified meta-learning framework that systematically integrates weak structural priors (translation equivariance, locality) with strong physical priors (governing equations and boundary conditions). BSNP addresses two critical obstacles: discretization overfitting through stochastic collocation that resamples residual evaluation points, and uncertainty collapse through mean-field enforcement that applies PDE constraints only to predictive means while preserving learned uncertainty. Comprehensive experiments on nonlinear Poisson equations, Burgers dynamics, and Navier-Stokes flows demonstrate that BSNP achieves superior accuracy and well-calibrated uncertainty quantification in sparse-data regimes.

Deep Learning · Large Language Models

Mihir Prabhudesai, Aryan Satpathy, Yangmin Li, Zheyang Qin, Nikash Bhardwaj, Amir Zadeh, Chuan Li, Katerina Fragkiadaki, Deepak Pathak

We have witnessed remarkable advances in LLM reasoning capabilities with the advent of DeepSeek-R1. However, much of this progress has been fueled by the abundance of internet question–answer (QA) pairs—a major bottleneck going forward, since such data is limited in scale and concentrated mainly in domains like mathematics. In contrast, other sciences such as physics lack sufficient large-scale QA datasets to effectively train reasoning-capable models. In this work, we show that physics simulators can serve as a powerful alternative source of supervision for training LLMs for physical reasoning. We generate random scenes in physics engines, create synthetic question–answer pairs from simulated interactions, and train LLMs using reinforcement learning on this synthetic data. Our models exhibit zero-shot sim-to-real transfer to real-world physics benchmarks: for example, training solely on synthetic simulated data improves performance on IPhO (International Physics Olympiad) problems by 5–10 percentage points across different model sizes. These results demonstrate that physics simulators can act as scalable data generators, enabling LLMs to acquire deep physical reasoning skills beyond the limitations of internet-scale QA data.

Applications · Computer Vision

Nils Morbitzer, Jonathan Evers, Artem Savkin, Thomas Stauner, Nassir Navab, Federico Tombari, Stefano Gasperini

Forecasting the evolution of dynamic environments is crucial for autonomous agents. While generative world models have recently achieved high photorealism in 2D video synthesis, by mixing within the image plane ego-motion and environmental dynamics, they exhibit physical inconsistencies, such as morphing or vanishing objects, especially over long time horizons. In this paper, we propose FR3D, a world model that predicts a persistent 3D latent representation for future dynamic 3D reconstruction. Unlike prior works that treat the world as a sequence of image-based features, FR3D explicitly decouples the 3D evolution of the scene from the agent's trajectory, treating the inferred ego-motion as a latent proxy for action. This disentanglement resolves the ambiguities between self-motion and world-motion, ensuring geometric consistency into the future. Furthermore, we introduce a teacher-student distillation strategy that leverages the spatial "common sense" of off-the-shelf foundation models, leading to robust zero-shot generalization. Extensive experiments demonstrate FR3D's strong performance for future dynamic 3D reconstruction from monocular observations across multiple datasets, even 2 seconds into the future.

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.

Reinforcement Learning · Multi-agent

Xuhui Kang, Sung-Wook Lee, Haolin Liu, Yuyan Wang, Yen-Ling Kuo

The ability to adapt to physical actions and constraints in an environment is crucial for embodied agents (e.g., robots) to effectively collaborate with humans. Such physically grounded human-AI collaboration must account for the increased complexity of the continuous state-action space and constrained dynamics caused by physical constraints. However, most existing collaboration benchmarks are discrete or do not consider physical attributes and constraints. To address this, we introduce Moving Out, a human-AI collaboration benchmark that resembles a wide range of collaboration modes affected by physical attributes and constraints, such as moving heavy items together and coordinating actions to move an item around a corner. Moving Out consists of two challenges and human-human interaction data to comprehensively evaluate models' abilities to adapt to diverse human behaviors and unseen physical attributes. To give embodied agents the capability to collaborate with humans under physical attributes and constraints, we propose a novel method, BASS (Behavior Augmentation, Simulation, and Selection), to enhance the diversity of agents and their understanding of the outcome of actions. We systematically compare BASS and state-of-the-art models in AI-AI and human-AI experiments, showing that BASS can effectively collaborate with both unseen AI and humans.

Applications · Time Series

Hua Wang, Xianhao Jiao, Fan Zhang

Deep forecasting models often suffer from attenuated periodic perception and entangled trend–noise representations as network depth increases. Moreover, the widely adopted channel-independent paradigm, while improving training stability, disrupts intrinsic dynamic coordination among variables, hindering the modeling of cross-variable consistency in multivariate time series. To address these issues, we propose PESD-TSF, a physics-inspired structured decomposition framework for long-term time series forecasting that jointly emphasizes interpretability and predictive accuracy. PESD-TSF introduces three key designs. First, a Multiplicative Periodic Gating mechanism incorporates continuous-time priors to dynamically modulate signal amplitudes, preserving periodic structures across deep layers. Second, a multi-scale structured encoder integrates detrended attention with hierarchical sampling to explicitly decouple long-term trends from high-frequency variations while retaining fine-grained temporal semantics. Third, to recover disrupted inter-variable dependencies, we propose Cross-Scale Collaborative Attention (CSCA) together with an RLC regularization scheme, which reconstructs global inter-variable topology in deep feature spaces and enforces physically consistent collaboration through orthogonality and consistency constraints. Extensive experiments on benchmark datasets from multiple domains demonstrate that PESD-TSF consistently achieves state-of-the-art performance, with particularly strong gains on multivariate forecasting tasks involving complex inter-variable coupling, highlighting its superior structural modeling capability and generalization.

Deep Learning · Large Language Models

Chenxiao Yang, Nati Srebro, Zhiyuan Li

Modern language models reason within bounded attention size, a physical constraint that poses a fundamental barrier to long-horizon reasoning. We identify recursion as a core principle for overcoming this barrier, and propose recursive models as a minimal realization, where the model can recursively invoke itself to solve subtasks in sequences that are contextually isolated. We prove that any computable problem admits a recursive decomposition where subtasks require only exponentially smaller active context than standard autoregressive models, and this approach strictly surpasses any single-context management approaches such as summarization. We further show that modern agentic systems are naturally suited for realizing recursion in a generalized way where arbitrary processing of contexts and workflows is allowed, and prove they can achieve the same power as recursive models, yet none can surpass it. Experimentally, we train a 3B model to learn recursive reasoning and evaluate on SAT, finding that it significantly outperforms frontier LLMs.

Deep Learning · Large Language Models

Udari Sehwag, Elaine Lau, Haniyeh Oskouie, Shayan Shabihi, Erich Liang, Andrea Toledo, Guillermo Mangialardi, Sergio Fonrouge, Ed-Yeremai Hernandez-Cardona, Paula Vergara 等

Accelerating scientific discovery requires the identification of which experiments would yield the best outcomes before committing resources to costly physical validation. While existing benchmarks evaluate LLMs on scientific knowledge and reasoning, their ability to predict experimental outcomes---a task where AI could significantly exceed human capabilities---remains largely underexplored. We introduce SciPredict, a benchmark comprising 405 tasks derived from recent empirical studies in 33 specialized sub-fields of physics, biology, and chemistry. SciPredict addresses two critical questions: (a) *can LLMs predict the outcome of scientific experiments with sufficient accuracy?* and (b) *can such predictions be reliably used in the scientific research process?* Evaluations reveal fundamental limitations on both fronts. Model accuracies are 14-26\% and human expert performance is $\approx$20\%. Although some frontier models exceed human performance model accuracy is still far below what would enable reliable experimental guidance. Even within the limited performance, models fail to distinguish reliable predictions from unreliable ones, achieving only $\approx$20\% accuracy regardless of their confidence or whether they judge outcomes as predictable without physical experimentation. Human experts, in contrast, demonstrate strong calibration: their accuracy increases from $\approx$5\% to $\approx$80\% as they deem outcomes more predictable without conducting the experiment. SciPredict establishes a rigorous framework demonstrating that superhuman performance in experimental science requires not just better predictions, but better awareness of prediction reliability. For reproducibility all our data and code are provided at https://anonymous.4open.science/r/SciPredict-AI01.

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.

Deep Learning · Foundation Models

jing wu, Jianhua Wu, Jiayi Guan, Jiahong Chen, Jinghui Lu, Hangjun Ye, Bingzhao Gao, Long Chen

Vision-Language Models (VLMs) perform well on commonsense reasoning tasks but struggle with visual spatial reasoning. Most existing solutions introduce extra 3D priors or external spatial encoders, which increase complexity and degrade the underlying VLMs' general-purpose capabilities after spatial fine-tuning. To this end, we propose a parameter-efficient \textit{\textbf{Spatio}-vision \textbf{L}anguage \textbf{M}odels (SpatioLM)}, that enhances spatial intelligence without extra 3D priors or third-party spatial encoders. Concretely, we design a plug-and-play and non-invasive spatio-vision module that elicits the spatial knowledge inherent in VLMs. Furthermore, we innovatively leverage pseudo depth and camera information as supervision to guide the model in learning physically coherent representations. Extensive experiments show that SpatioLM achieves significant improvements in diverse tasks, including spatial perception and understanding while maintains the general-purpose capabilities. Notably, the model achieves an impressive score of 71.6 on the VSI-Bench (the first model to surpass 70). In addition, it attains competitive performance when transferred to embodied manipulation tasks.

Deep Learning · Large Language Models

Bo Zhang, Jinfeng Zhou, Yuxuan Chen, Jianing Yin, Minlie Huang, Hongning Wang

Large Language Models (LLMs) have shown significant potential in scientific discovery but struggle to bridge the gap between theoretical reasoning and verifiable physical simulation. Existing solutions operate in a passive "execute-then-response" loop and thus lack runtime perception, obscuring agents to transient anomalies (e.g., numerical instability or diverging oscillations). To address this limitation, we propose EmbodiedAct, a framework that transforms established scientific software into active embodied agents by grounding LLMs in embodied actions with a tight perception-execution loop. We instantiate EmbodiedAct within MATLAB and evaluate it on complex engineering design and scientific modeling tasks. Extensive experiments show that EmbodiedAct significantly outperforms existing baselines, achieving SOTA performance by ensuring satisfactory reliability and stability in long-horizon simulations and enhanced accuracy in scientific modeling.

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.