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Applications · Chemistry, Physics, and Earth Sciences

Fengzhe Zhang, Laurence Midgley, Jose Miguel Hernandez-Lobato

Score-based diffusion models (SBDMs) are powerful amortized samplers for Boltzmann distributions; however, imperfect score estimates bias downstream Monte Carlo estimates. Classical importance sampling (IS) can correct this bias, but computing exact likelihoods requires solving the probability-flow ordinary differential equation (PF–ODE), a procedure that is prohibitively costly and scales poorly with dimensionality. We introduce Variance-Tuned Diffusion Importance Sampling (VT-DIS), a lightweight post-training method that adapts the per-step noise covariance of a pretrained SBDM by minimizing the $\alpha$-divergence $(\alpha=2)$ between its forward diffusion and reverse denoising trajectories. VT-DIS assigns a single trajectory-wise importance weight to the joint forward–reverse process, yielding unbiased expectation estimates at test time with negligible inference-time overhead compared to standard sampling. On the DW-4, LJ-13, and alanine-dipeptide benchmarks, VT-DIS achieves effective sample sizes of approximately 80%, 35%, and 3.5%, respectively, while using only a fraction of the computational budget required by vanilla diffusion + IS or PF-ODE–based IS.

Applications · Chemistry, Physics, and Earth Sciences

Jaemin Seo, Su Rin Lee, JaeYong Lee

Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler–Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods.

Applications · Chemistry, Physics, and Earth Sciences

Minkyu Kim, Nayoung Kim, Honghui Kim, Sungsoo Ahn

Discovering heterogeneous catalysts tailored for specific reaction intermediates remains a fundamental bottleneck in materials science. While traditional trial-and-error methods and recent generative models have shown promise, they struggle to capture the intrinsic coupling between surface geometry and adsorbate interactions. To address this limitation, we propose CatFlow, a flow matching-based framework for de novo design and structure prediction of heterogeneous catalysts. Our model operates on a primitive cell-based factorized representation of the slab-adsorbate complex, reducing the number of learnable variables by an average of 9.2x while explicitly encoding the surface orientation of the slab-adsorbate interface. Experiments on the Open Catalyst 2020 dataset demonstrate that CatFlow significantly improves the structural fidelity of generated catalysts compared to autoregressive and sequential baselines. Further experiments show that the generated structures accurately capture the adsorption energy distributions of physically plausible interfaces and lie closer to thermodynamic local minima.

Applications · Chemistry, Physics, and Earth Sciences

Guoze Sun, Tianya Miao, Haoyang Huang, Huaguan Chen, Han Wan, Rui Zhang, Hao Sun

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (GANO), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. GANO encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-injected surrogate provides a reliable gradient pathway for geometry updates. Moreover, GANO supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to $+55.9\%$ lift-to-drag improvement for airfoils and $\sim 7\%$ drag reduction for vehicles.

Applications · Chemistry, Physics, and Earth Sciences

Pietro Sittoni, Emanuele Zangrando, Angelo Alberto Casulli, Nicola Guglielmi, Francesco Tudisco

Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availability of high-performance computing infrastructure, many critical applications remain constrained by the substantial computational costs associated with generating large-scale, high-quality datasets and training models. In this work, inspired by studies on the structure of Green's functions for elliptic PDEs, we introduce Neural-HSS, a parameter-efficient architecture built upon the Hierarchical Semi-Separable (HSS) matrix structure that is provably data-efficient for a broad class of PDEs. We theoretically analyze the proposed architecture, proving that it satisfies exactness properties even in very low-data regimes. We also investigate its connections with other architectural primitives, such as the Fourier neural operator layer and convolutional layers. We experimentally validate the data efficiency of Neural-HSS on the three-dimensional Poisson equation over a grid of two million points, demonstrating its superior ability to learn from data generated by elliptic PDEs in the low-data regime while outperforming baseline methods. Finally, we demonstrate its capability to learn from data arising from a broad class of PDEs in diverse domains, including electromagnetism, fluid dynamics, and biology.

Applications · Chemistry, Physics, and Earth Sciences

Mohammad Rashed, Duarte Filipe Valoroso Madeira, Babak Gholami, Caglar Guerbuez, Yunjia Yang, Nils Thuerey

Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. We further benchmark against competitive baselines, and find the same ordering of conditioning signals and the same OOD trends. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations.

Applications · Chemistry, Physics, and Earth Sciences

Sung Moon Ko, Jaewan Lee, Sumin Lee, Soorin Yim, Sehui Han

Geometrical interpretations of deep learning models offer insightful perspectives into their underlying mathematical structures. In this work, we introduce a novel approach that leverages differential geometry, particularly concepts from Riemannian geometry, to integrate multiple models into a unified transfer learning framework. By aligning the Ricci curvature of latent space of individual models, we construct an interrelated architecture, namely Geometric Embedding Alignment via cuRvature matching in transfer learning (GEAR), which ensures comprehensive geometric representation across datapoints. This framework enables the effective aggregation of knowledge from diverse sources, thereby improving performance on target tasks. We evaluate our model on 23 molecular task pairs and demonstrate significant performance gains over existing benchmark models—achieving improvements of at least 14.4% under random splits and 8.3% under scaffold splits.

Applications · Chemistry, Physics, and Earth Sciences

Jacopo Teneggi, SM Turzo, Tanya Marwah, Alberto Bietti, P. Douglas Renfrew, Vikram Mulligan, Siavash Golkar

Large language models (LLMs) are capable of emulating reasoning and using tools, creating opportunities for autonomous agents that execute complex scientific tasks. Protein design provides a natural testbed: although machine learning (ML) methods achieve strong results, these are largely restricted to canonical amino acids and narrow objectives, leaving unfilled need for a generalist tool for broad design pipelines. We introduce Agent Rosetta, an LLM agent paired with a structured environment for operating Rosetta, the leading physics-based heteropolymer design software, capable of modeling non-canonical building blocks and geometries. Agent Rosetta iteratively refines designs to achieve user-defined objectives, combining LLM reasoning with Rosetta's generality. We evaluate Agent Rosetta on design with canonical amino acids, matching specialized models and expert baselines, and with non-canonical residues-where ML approaches fail-achieving comparable performance. Critically, prompt engineering alone often fails to generate Rosetta actions, demonstrating that environment design is essential for integrating LLM agents with specialized software. Our results show that properly designed environments enable LLM agents to make scientific software accessible while matching specialized tools and human experts.

Applications · Chemistry, Physics, and Earth Sciences

Liao Chang, Luotian Yuan, Yiping Ke, Ying Wei

Multi-step retrosynthesis planning is a fundamental challenge in organic chemistry, defined by its enormous search space. Existing methods typically formulate it as a Markov Decision Process (MDP) with a fixed choice of transition model (i.e., a single-step retrosynthesis model), and focus on improving *how to search* through better policies and value functions. However, *how the transition space itself is navigated* remains largely unexplored. This limitation is particularly urgent given our observation of pronounced *skill disparity* among single-step prediction models: different models exhibit substantially different performance across molecule states. Motivated by this observation, we introduce RetrOrchestrator, an LLM-powered agent that explicitly accounts for model skill disparity by reframing retrosynthesis planning as a Partially Observable Markov Decision Process (POMDP). By regarding each single-step prediction model as a tool, we further propose a scaffold-aware reinforcement learning algorithm to optimize navigation policy within the transition space. As a result, RetrOrchestrator jointly searches which molecule to expand and which single-step model to apply for the molecule at the current step. Empirically, RetrOrchestrator significantly outperforms static baselines on the Retro*-190 benchmark, achieving a state-of-the-art 94.21\% success rate as well as a Pareto front in both wallclock time and number of model queries.

Applications · Chemistry, Physics, and Earth Sciences

Mujie Lin, Yutian Liu, Yudi Guo, Yanzhen Hou, Yiheng Tao, Ruochong Zheng, Kaiwen Cheng, Xin Shan, Youdong Mao, Jie Chen

Generating long-horizon, all-atom molecular dynamics (MD) is difficult due to error accumulation in time-domain autoregressive models (causing drift) and fixed step-size constraints on temporal resolution. We propose **BioDynaSpec**, which reformulates protein dynamics as spatio-spectral generation: **Independent Windowed Fourier Decomposition (IWFD)** decomposes trajectories into independent windowed frequency representations, and a generator combines low-to-high frequency autoregression with diffusion denoising to reconstruct continuous motion. We introduce **Inter-Residue Frequency Coupling (IRFC)** bias, a learnable Gaussian distance bias in attention that injects a resonance-inspired structural prior to stabilize training and improve cross-residue, cross-frequency consistency. On ATLAS, BioDynaSpec improves 250-frame trajectory generation with $R_{250}=1.509$ Å (where $R_s$ denotes the mean per-frame C$\alpha$-RMSE over the first $s$ frames after alignment), reducing error by 60.4\% vs. MDGEN and 57.2\% vs. ProAR, and achieves the best PCA-2D displacement-profile correlation and stepwise distribution matching. For equilibrium conformational sampling, it achieves Root Mean $W_2=1.31$, MD PCA $W_2=0.90$, and Joint PCA $W_2=1.19$ (50.03\%, 35.25\%, and 47.58\% lower than the next best), while ablations show removing IRFC severely degrades RMSE/MAE and correlation.

Applications · Chemistry, Physics, and Earth Sciences

Shrimon Mukherjee, KISHALAY DAS, Partha Basuchowdhuri, Pawan Goyal, Niloy Ganguly

Fast and accurate prediction of crystal properties is a central challenge in new materials design. Graph Neural Networks and transformer-based models have emerged as powerful tools for this task due to their ability to encode the local structural environment of atoms within a crystal. However, these models are data hungry and in practice labeled data for crystal properties are very scarce. Pretrain–finetuning strategies, particularly those based on diffusion models, have shown promise in addressing these limitations. In this work, we introduce a novel latent-diffusion based pretraining framework CrysLDNet designed to mitigate the data scarcity issue. Our approach integrates a Variational Autoencoder (VAE) with a diffusion model during the pretraining stage. The VAE encoder maps 3D crystal structures into a smooth latent space, within which the diffusion process is applied. This latent diffusion pretraining enables the graph encoder to effectively capture structural and chemical semantics from large-scale unlabeled data, which can then be finetuned for specific property prediction tasks. Comprehensive experiments on popular DFT datasets for property prediction reveal that CrysLDNet significantly outperforms both training-from-scratch and pretrained baselines, with improvements of 4.26% and 4.90% on JARVIS and MP datasets. Additionally, the learned representations remain robust under sparse data conditions and are expressive enough to correct DFT errors when finetuned with limited experimental data.

Applications · Chemistry, Physics, and Earth Sciences

Zipeng Sun, Can Chen, Ye Yuan, Haolun Wu, Jiayao Gu, Christopher Pal, Xue Liu

We study offline black-box optimization (BBO), aiming to discover improved designs from an offline dataset of designs and labels, a problem common in robotics, DNA, and materials science with limited labeled samples. While recent work applies autoregressive LLMs to BBO by formatting tasks as natural-language prompts, their left-to-right design generation struggles to capture the strong bidirectional dependencies inherent in design problems. To address this, we propose adapting diffusion LLMs to offline BBO to leverage their bidirectional modeling capabilities. However, a domain gap exists between the natural text pre-training of diffusion LLMs and the heterogeneous signals in BBO (prompts, designs, and labels). To bridge this gap, we construct a unified prompt–response corpus and introduce delimiter tokens to explicitly mark field boundaries for *domain adaptation*. We further propose a two-stage *post-training* framework to align the diffusion LLM generation with high-label designs. The first stage performs supervised fine-tuning on the unified dataset via masked-response prediction, and the second stage adopts reinforcement learning with rewards defined by label improvements. Our method achieves state-of-the-art results on Design-Bench small-data settings. Code for our work is available here: https://anonymous.4open.science/r/Anonymous-dllm4bbo-D78A/README.md.

Applications · Chemistry, Physics, and Earth Sciences

Weilong Chen, Bojun Zhao, Jan Eckwert, Julija Zavadlav

Sampling equilibrium molecular configurations from the Boltzmann distribution is a longstanding challenge. Boltzmann Generators (BGs) address this by combining exact-likelihood generative models with importance sampling, but their practical scalability is limited. Meanwhile, coarse-grained surrogates enable the modeling of larger systems by reducing effective dimensionality, yet often lack the reweighting process required to ensure asymptotically correct statistics. In this work, we propose Coarse-Grained Boltzmann Generators (CG-BGs), a principled framework that unifies scalable reduced-order modeling with the exactness of importance sampling. CG-BGs act in a coarse-grained coordinate space, using a learned potential of mean force (PMF) to reweight samples generated by a flow-based model. Crucially, we show that this PMF can be efficiently learned from rapidly converged data via force matching. Our results demonstrate that CG-BGs faithfully capture complex interactions mediated by explicit solvent within highly reduced representations, establishing a scalable pathway for the unbiased sampling of larger molecular systems.

Applications · Chemistry, Physics, and Earth Sciences

Xin Ju, Hadrian Fung, Yuyan Zhang, Carl Jacquemyn, Matthew Jackson, Randolph Settgast, Sally Benson, Gege Wen

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical simulations of these systems are notoriously computationally expensive due to geological heterogeneity, high resolution requirements, and the tight coupling of physical processes with distinct propagation time scales. Here we propose the Adaptive Physics Transformer (APT), a geometry-, mesh-, and physics-agnostic neural operator that explicitly addresses these challenges. APT fuses a graph-based encoder to extract high-resolution local heterogeneous features with a global attention mechanism to resolve long-range physical impacts. Our results demonstrate that APT outperforms state-of-the-art architectures in subsurface tasks across both regular and irregular grids with robust super-resolution capabilities. Notably, APT is the first architecture that directly learns from adaptive mesh refinement simulations. We also demonstrate APT's capability for cross-dataset learning, positioning it as a robust and scalable backbone for large-scale subsurface foundation model development.

Applications · Chemistry, Physics, and Earth Sciences

Yaotian Yang, Yiwen Tang, Yizhe Chen, Xiao Chen, Jiangjie Qiu, Hao Xiong, Haoyu Yin, Zhiyao Luo, Yifei Zhang, Sijia Tao 等

Reconstructing atomistic crystal structures from a single noisy STEM projection is an ill-posed inverse problem: multiple lattices can explain similar contrast, and purely feed-forward models cannot verify physical validity. We present **AutoMat**, a failure-aware agentic *controller* that performs inference-time hypothesis search with *closed-loop verification* to convert Scanning Transmission Electron Microscopy (STEM) images into simulation-ready crystal structures and downstream properties. AutoMat composes perception and physics modules—pattern-adaptive denoising, physics-guided template retrieval (as a fallback), symmetry-constrained atomic reconstruction, and MLIP-based relaxation/validation—and triggers rollback-and-retry when verification fails. For systematic evaluation, we introduce **STEM2Mat-Bench**, a benchmark dataset containing 450+ annotated samples. Performance is assessed using lattice root-mean-square deviation (RMSD), formation energy mean absolute error (MAE), and structure matching accuracy. Results demonstrate that AutoMat outperforms existing approaches including SOTA models, specialized domain tools, and closed-source multimodal large models. This work establishes a direct pathway from microscopic characterization to atomic-scale modeling, addressing a fundamental challenge in materials science.

Applications · Chemistry, Physics, and Earth Sciences

Jephte Abijuru, Mayank Kumar Nagda, Phil Sidney Ostheimer, Jan Tauberschmidt, Sebastian Vollmer, Stephan Mandt, Marius Kloft, Sophie Fellenz

Physics-informed neural networks (PINNs) enforce physical laws by minimizing partial differential equation (PDE) residuals and auxiliary constraints. Standard training relies on a mean-squared error (MSE) objective, which implicitly assumes independent Gaussian residuals with a fixed global variance. We show theoretically and empirically that residuals encountered during PINN training are heterogeneous and heavy-tailed, revealing a systematic mismatch with this assumption. As a consequence, a small number of large residuals can disproportionately dominate both the loss and gradient, leading to poorly balanced optimization dynamics. Motivated by this mismatch, we adopt a Student-$t$ residual model to explicitly capture heavy-tailed behavior. An equivalent hierarchical representation yields an expectation–maximization (EM) algorithm that alternates between estimating residual-dependent weights and optimizing network parameters via a weighted MSE objective, allowing existing PINN solvers to be reused in the M-step. The resulting training dynamics bound the influence of extreme residuals and admit almost sure convergence guarantees under standard stochastic optimization assumptions. Experiments across a diverse suite of challenging PDE benchmarks demonstrate consistently improved solution accuracy and robustness compared to standard PINN training.

Applications · Chemistry, Physics, and Earth Sciences

Jephte Abijuru, Mayank Kumar Nagda, Phil Sidney Ostheimer, Sebastian Vollmer, Marius Kloft, Sophie Fellenz

Physics-Informed Neural Networks (PINNs) embed physical laws into deep learning models. However, conventional PINNs often suffer from failure modes leading to inaccurate solutions. We trace these failure modes to two structural pathologies: gradient shattering, where gradients degrade with depth and provide little training signal, and flow mismatch, where training pushes predictions along trajectories that diverge from the PDE solution path. We introduce ResPINNs, which reformulate PINNs as residual flows, networks that iteratively refine their own predictions through explicit corrective steps, in the spirit of classical iterative solvers. Our analysis shows that this design mitigates both pathologies by keeping updates aligned with descent and by preserving informative gradients across depth. Extensive experiments on PDE benchmarks confirm that ResPINNs achieve higher accuracy with substantially fewer parameters than conventional architectures.

Applications · Chemistry, Physics, and Earth Sciences

Martin Andrae, Erik Larsson, So Takao, Tomas Landelius, Fredrik Lindsten

Data assimilation (DA) is a cornerstone of scientific and engineering applications, combining model forecasts with sparse and noisy observations to estimate latent system states. Classical high-dimensional DA methods, such as the ensemble Kalman filter, rely on Gaussian approximations that are violated for complex dynamics or observation operators. To address this limitation, we introduce DAISI, a scalable filtering algorithm built on flow-based generative models that enables flexible probabilistic inference using data-driven priors. The core idea is to use a stationary, pre-trained generative prior that first incorporates forecast information through a novel *inverse-sampling step*, before assimilating observations via guidance-based conditional sampling. This allows us to leverage any forecasting model as part of the DA pipeline without having to retrain or fine-tune the generative prior at each assimilation step. Experiments on challenging nonlinear systems show that DAISI achieves accurate filtering results in regimes with sparse, noisy, and nonlinear observations where traditional methods struggle.

Applications · Chemistry, Physics, and Earth Sciences

Ryan Liu, Eric Qu, Tobias Kreiman, Samuel Blau, Aditi Krishnapriyan

Machine Learning Interatomic Potentials (MLIPs) sometimes fail to reproduce the physical smoothness of the quantum potential energy surface (PES), leading to erroneous behavior in downstream simulations that can be missed by standard energy and force regression evaluations. Existing evaluations, such as microcanonical molecular dynamics (MD), are computationally expensive and primarily probe near-equilibrium states. To improve evaluation metrics for MLIPs, we introduce the Bond Smoothness Characterization Test (BSCT). This efficient benchmark probes the PES via controlled bond deformations and detects instabilities, including discontinuities, artificial minima, and spurious forces, both near and far from equilibrium. We show that BSCT correlates strongly with MD stability at a fraction of the cost. To demonstrate how BSCT can guide iterative model design, we use an unconstrained Transformer backbone as a testbed, showing how refinements like differentiable $k$-nearest neighbors and temperature-controlled attention systematically reduce artifacts identified by the metric, resulting in an MLIP that simultaneously achieves strong accuracy and physical soundness. Our results establish BSCT as an "in-the-loop" proxy that alerts MLIP developers to physical challenges that are not captured by current MLIP evaluations.

Applications · Chemistry, Physics, and Earth Sciences

Eric Qu, Brandon Wood, Aditi Krishnapriyan, Zachary Ulissi

Machine-learning interatomic potentials (MLIPs) have advanced rapidly, with many top models relying on strong physics-based inductive bias. However, as models scale to larger systems like biomolecules and electrolytes, they struggle to accurately capture long-range (LR) interactions, leading current approaches to rely on explicit physics-based terms or components. In this work, we propose AllScAIP, a straightforward, attention-based, and energy-conserving MLIP model that scales to O(100 million) training samples. It addresses the long-range challenge using an all-to-all node attention component that is purely data-driven. Extensive ablations reveal that in low-data/small-model regimes, inductive biases improve sample efficiency. However, as data and model size scale, these benefits diminish or even reverse, while all-to-all attention remains critical for capturing LR interactions. Our model achieves state-of-the-art energy/force accuracy on molecular systems (OMol25), while being competitive on materials (OMat24) and catalysts (OC20). Furthermore, it enables stable, long-timescale MD simulations that accurately recover experimental observables, including density and heat of vaporization predictions.