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Applications · Chemistry, Physics, and Earth Sciences

Mauricio Montes, Grégoire Sergeant-Perthuis

Programming adaptive behaviors at the cellular level is a long-standing goal that raises the question of how probabilistic computation can be implemented in biochemical systems. Chemical reaction networks (CRNs) provide such a substrate and have been shown to realize probabilistic models, including hidden Markov models and factor graphs, with dynamics reproducing Bayesian inference and belief propagation. However, encoding these algorithms typically requires prohibitively large reaction networks, and classical CRN reduction techniques don't apply. By embedding CRNs into factor graphs in a structure- and dynamics-preserving manner, we leverage recent factor-graph reduction results to obtain significantly smaller CRNs, a gain we demonstrate numerically.

Applications · Chemistry, Physics, and Earth Sciences

Eike S. Eberhard, Luca Anthony Thiede, Abdulrahman Aldossary, Andreas Burger, Nicholas Gao, Vignesh Bhethanabotla, Alan Aspuru-Guzik, Stephan Günnemann

Machine-learned (ML) XC-functionals promise improved accuracy, but overfit to training energies and basis sets without proper regularization. We introduce Derivative Informed XC-Loss (DI-Loss), a loss that regularizes ML-XC training by supervising energy gradients on the Grassmannian of density matrices. Crucially, rather than merely matching the self-consistent fixed point, DI-Loss forces the dynamics of the SCF process to align with the target functional. Across all evaluated architectures, this improves basis set generalization and electron densities. Distilling hybrid ($\mathcal{O}(N^4)$-scaling) functionals to $\mathcal{O}(N^3)$-scaling ML-XC functionals, we observe a $>60\%$ reduction in energy MAE compared to energy and density supervision alone, while simultaneously reducing the density-dipole error by 65\%. We show that initializing from these distilled functionals can reduce hybrid SCF iterations by up to 55\%. Furthermore, DI-Loss improves TDDFT excited-state predictions by approximately 30\%.

Applications · Chemistry, Physics, and Earth Sciences

hao chen, Tao Han, Jie ZHANG, Song Guo, Fenghua Ling, LEI BAI

Long-term weather forecasting is critical for socioeconomic planning and disaster preparedness. While recent approaches employ finetuning to extend prediction horizons, they remain constrained by the issues of catastrophic forgetting, error accumulation, and high training overhead. To address these limitations, we present a novel pipeline across pretraining, finetuning and forecasting to enhance long‑context modeling while reducing computational overhead. First, we introduce an Efficient Multi‑scale Transformer (EMFormer) to extract multi‑scale features through a single convolution in both training and inference. Based on the new architecture, we further employ an accumulative context finetuning to improve temporal consistency without degrading short‑term accuracy. Additionally, we propose a composite loss that dynamically balances different terms via a sinusoidal weighting, thereby adaptively guiding the optimization trajectory throughout pretraining and finetuning. Experiments show that our approach achieves great performance in weather forecasting and extreme event prediction, substantially improving long-term forecast accuracy. Moreover, EMFormer demonstrates strong generalization on vision benchmarks (ImageNet-1K and ADE20K) while delivering a 5.69$\times$ speedup over conventional multi-scale modules.

Applications · Chemistry, Physics, and Earth Sciences

Kexin Zhang, Weichen Qin, Yue Teng, Jiale Yu, Yuanyuan Ma, jinyu lin, Liping Sun, Jie Zheng, Jingyi Yu

The emergence of Vibe Researching is transforming scientific research into an interactive workflow, where agents orchestrate complex tasks via the Model Context Protocol (MCP). In this ecosystem, scientific tools must evolve from offline simulators into responsive Agent Skills. However, diffusion-based protein docking models—a core component of the current deep learning infrastructure for structural biology—suffer from excessively high latency, rendering them incompatible with real-time agentic interaction. To bridge this gap, we present a compute-efficient vertical foundation model that synergizes architectural optimization with generative consistency. First, we leverage Progressive Consistency Regularization (PCR) to compress complex generative dynamics into a few-step predictor, achieving sub-second latency. Second, we propose Residual Quantization, using mixed-precision on residual streams to alleviate memory bottlenecks while preserving numerical precision. Our approach achieves state-of-the-art (SOTA) docking accuracy while attaining a two-order-of-magnitude speedup ($>300\times$) over AlphaFold3, establishing a new efficiency standard for high-throughput virtual screening. By transforming molecular docking into an interactive, real-time tool, this work establishes a scalable, deep-learning infrastructure for the next generation of AI-driven drug discovery.

Applications · Chemistry, Physics, and Earth Sciences

Zhuoran Li, Xu Sun, Wanyu LIN, Chang Chen

Controllable molecule generation is crucial for diverse scientific applications, such as drug discovery and materials design. While large language models (LLMs) show great promise, their dense and entangled representations impede precise control over the generation of molecules with bespoke substructures or properties. To address this, we propose Sparse Representation Editing (SpaRE), an interpretability-driven framework for fine-grained and precise control in LLM-based molecule generation. The crux of SpaRE is to learn an overcomplete sparse feature space that disentangles LLM representations into a compact set of latent features corresponding to chemically meaningful concepts. Within this space, we can directly manipulate these concept-aligned latent features to achieve (1) local control, by generating target atoms and functional groups at specified positions; and (2) global control, by customizing the overall structural and physicochemical properties within defined ranges. In this way, our framework advances interpretability from post-hoc analysis to actionable generative control. Experiments show that SpaRE can generate chemically desirable molecules under complex constraints in real-world scenarios, while offering mechanistic insights for quantitative structure–property analysis. The code and demo are available at https://github.com/SpaRE-paper/SpaRE.

Applications · Chemistry, Physics, and Earth Sciences

Haokai Hong, Wanyu LIN, KC Tan

Large-scale molecular dynamics simulations are essential in understanding chemical and biological processes, necessitating the accurate and efficient modeling of interatomic interactions. Existing learning-based methods generally are based on message passing mechanisms; they are either not scalable or too coarse to offer accurate modeling. We propose a new message passing framework that can effectively and efficiently model interatomic interactions for simulating large-scale molecular dynamics at full atomic resolution. Specifically, our framework is stacked with a sequence of message passing neural network layers, each realizing the message passing over a distinct and dilated star-structured path. These star-structured paths are constructed progressively along dilated regions to capture the distance-dependent interactions. The crux of our framework is that it resolves the problem of dense interatomic interactions of large-scale atomic systems with sparser and region-based message passing graphs. We evaluate the framework on four benchmarks: MD22 (molecules with 42–370 atoms), Chignolin (a 166-atom protein featuring diverse conformations), the AdK dataset (a protein trajectory with up to 3,000 atoms), and the MISATO dataset (over 10,000 heterogeneous protein-ligand complexes with systems up to 40,000 atoms). Comprehensive evaluations demonstrate that our approach delivers state-of-the-art performance overall across various benchmarks.

Applications · Chemistry, Physics, and Earth Sciences

Youngwoo Cho, Jaekak Yoo, Soyoung Yang, Dong-Joon Yi, Seung Lee, Mun Jeong, Jaegul Choo

The machine learning community has focused on computational efficiency, often leveraging lower-precision formats such as FP16, rather than the standard FP32. In contrast, little attention has been paid to higher-precision formats, such as FP64, despite their critical role in scientific domains like materials science, where even small numerical differences can lead to significant inaccuracies in physicochemical properties. This need for high precision extends to the emerging field of *machine learning for scientific tasks*, yet it has not been thoroughly investigated. According to several studies and our experiments, models trained with FP32 show insufficient accuracy compared to those trained with FP64, indicating that higher precision is also crucial in scientific machine learning, as in traditional scientific computing. This precision issue limits the potential of scientific machine learning that can replace the traditional scientific computing in practical research. Our position paper not only highlights these precision-related issues but also recommends reporting comparisons between FP32 and FP64 results, encouraging the release of FP64 models. We believe that these efforts can enable machine learning to contribute meaningfully to the natural sciences, ensuring both scientific reliability and practical applicability.

Applications · Chemistry, Physics, and Earth Sciences

Jonas Elsborg, Felix Aertebjerg, Luca Anthony Thiede, Alan Aspuru-Guzik, Tejs Vegge, Arghya Bhowmik

We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to analytically evaluate plane-wave coefficients via the Poisson summation formula. This formulation delegates non-local and periodic behavior to analytic transforms, enabling reconstruction of the full periodic charge density with a single inverse FFT. By avoiding explicit real-space grid probing, periodic image summation, and spherical harmonic expansions, ELECTRAFI matches or exceeds state-of-the-art accuracy across periodic benchmarks while being up to $633\times$ faster than the strongest competing method, reconstructing crystal charge densities in a fraction of a second. When used to initialize DFT calculations, ELECTRAFI reduces total DFT compute cost by up to $\sim$20 \%, whereas slower charge density models negate savings due to high inference times. Our results show that accuracy and inference cost jointly determine end-to-end DFT speedups, and motivate our focus on efficiency.

Applications · Chemistry, Physics, and Earth Sciences

Gnankan Landry Regis N'guessan, Bum Jun Kim

Physical systems near singularities, interfaces, and critical points exhibit power-law scaling, yet standard neural networks leave the governing exponents implicit. We introduce physics-informed M\"untz-Sz\'asz Networks (MSN-PINN), a power-law basis network that treats scaling exponents as trainable parameters. The model outputs both the solution and its scaling structure. We prove identifiability, or unique recovery, and show that, under these conditions, the squared error between learned and true exponents scales as $O(|\mu - \alpha|^2)$. Across experiments, MSN-PINN achieves single-exponent recovery with 1--5\% error under noise and sparse sampling. It recovers corner singularity exponents for the two-dimensional Laplace equation with 0.009\% error, matches the classical result of Kondrat'ev (1967), and recovers forcing-induced exponents in singular Poisson problems with 0.03\% and 0.05\% errors. On a 40-configuration wedge benchmark, it reaches a 100\% success rate with 0.022\% mean error. Constraint-aware training encodes physical requirements such as boundary condition compatibility and improves accuracy by three orders of magnitude over naive training. By combining the expressiveness of neural networks with the interpretability of asymptotic analysis, MSN-PINN produces learned parameters with direct physical meaning.

Applications · Chemistry, Physics, and Earth Sciences

Chuyang Xiang, Yichen Wei, Junchi Yan

Symbolic regression (SR) aims to discover interpretable mathematical expressions from observed data. While recent generative approaches have shown promise in treating SR as machine translation or multimodal learning tasks using NN methods, they suffer from a fundamental limitation: training-evaluation misalignment. The training objectives (average cross-entropy loss on a token level across the distribution of historical data) differ from the evaluation metric (fitting error for every test data / complexity), necessitating extensive heuristic post-processing and constant optimization. On the other hand, direct optimization methods suffer from curse of dimensionality, non-differentiability and local optima traps. We propose MOD-SR, unifying multimodal distribution learning during training with direct optimization at inference time. This is achieved by modeling the task as $p(x_0 \mid \mathcal{D}, y^*)$ and employing gradient-guided diffusion in embedding space, enhanced by contrastive learning and representation alignment. Furthermore, we introduce DFEX, a fixed-depth tree relaxation method that ensures differentiability for effective gradient guidance during inference. Experiments demonstrate significant improvements over existing methods, achieving superior performance on diverse benchmarks through a unified framework integrating distribution learning and optimization.

Applications · Chemistry, Physics, and Earth Sciences

Danyal Rehman, Charlie Tan, Yoshua Bengio, Joey Bose, Alexander Tong

Efficient sampling of molecular systems at thermodynamic equilibrium is a hallmark challenge in statistical physics. This challenge has driven the development of Boltzmann Generators (BGs), which allow rapid generation of uncorrelated equilibrium samples by combining a generative model with exact likelihoods and an importance sampling correction. However, modern BGs predominantly rely on Normalizing Flows (NFs), which either suffer from limited expressivity due to strict invertibility constraints (discrete time) or computationally expensive likelihoods (continuous time). In this paper, we propose Autoregressive Boltzmann Generators (ArBG), a novel autoregressive modelling framework that overcomes these limitations by departing from the flow-based BG paradigm. ArBG circumvents the topological constraints of flows and enables sequential inference-time interventions, while offering enhanced scalability by leveraging architectures effective in Large Language Models. We empirically demonstrate that ArBG leads to significant improvements over flow-based models across all benchmarks, but particularly in larger peptide systems such as the 10-residue Chignolin. Furthermore, we introduce Robin, a 132M parameter transferable model trained with the ArBG framework which improves over the previous state-of-the-art, reducing the zero-shot energy error, $\mathcal{E}$-$\mathcal{W}_2$, on 8-residue systems by $\sim 60$\%.

Applications · Chemistry, Physics, and Earth Sciences

Kiet Bennema ten Brinke, Koen Minartz, Vlado Menkovski

Simulating trajectories of dynamical systems is a fundamental problem in a wide range of fields such as molecular dynamics, biochemistry, and pedestrian dynamics. Machine learning has become an invaluable tool for scaling physics-based simulators and developing models directly from experimental data. In particular, recent advances in deep generative modeling and geometric deep learning enable probabilistic simulation by learning complex trajectory distributions while respecting intrinsic permutation and time-shift symmetries. However, trajectories of N-body systems are commonly characterized by high sensitivity to perturbations leading to bifurcations, as well as multi-scale temporal and spatial correlations. To address these challenges, we introduce STFlow (Spatio-Temporal Flow), a generative model based on graph neural networks and hierarchical convolutions. By incorporating data-dependent couplings within the Flow Matching framework, STFlow denoises starting from conditioned random-walks instead of Gaussian noise. This novel informed prior simplifies the learning task by reducing transport cost, increasing training and inference efficiency. We validate our approach on N-body systems, molecular dynamics, and human trajectory forecasting. Across these benchmarks, STFlow achieves the lowest prediction errors with fewer simulation steps and improved scalability.

Applications · Chemistry, Physics, and Earth Sciences

Sijie Zhao, Feng Liu, Xueliang Zhang, Hao Chen, Tao Han, JUNCHAO GONG, Ran Tao, Pengfeng Xiao, Xinyu Gu, LEI BAI

The increasing impact of climate change and extreme weather events has spurred growing interest in deep learning for weather research. However, existing studies often rely on weather data in pixel space, which presents several challenges such as smooth outputs in model outputs, limited applicability to a single pressure-variable subset (PVS), and high data storage and computational costs. To address these challenges, we propose a novel Weather Latent Autoencoder (WLA) that transforms weather data from pixel space to latent space, enabling efficient data representation. By decoupling weather reconstruction from downstream tasks, WLA improves the accuracy and sharpness of weather task model results. The incorporated Pressure-Variable Unified Module transforms multiple PVS into a unified representation, enhancing the adaptability of the model in multiple weather scenarios. Furthermore, weather tasks can be performed in a low-storage latent space of WLA rather than a high-storage pixel space, thus significantly reducing data storage and computational costs. Through extensive experimentation, we demonstrate its superior compression and reconstruction performance, enabling the creation of the ERA5-Latent dataset with unified representations of multiple PVS from ERA5 data. The compressed full PVS in the ERA5-Latent dataset reduces the original 244.34 TB of data to 0.43 TB. The downstream task further demonstrates that task models can apply to multiple PVS with low data costs in latent space and achieve superior performance compared to models in pixel space.

Applications · Chemistry, Physics, and Earth Sciences

Winfried Ripken, Michael Plainer, Gregor Lied, Thorben Frank, Oliver Unke, Stefan Chmiela, Frank Noe, Klaus-robert Mueller

Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn *Hamiltonian Flow Maps* by predicting the *mean* phase-space evolution over a chosen time span $\Delta t$, enabling stable large-timestep updates far beyond the stability limits of classical integrators. To this end, we impose a *Mean Flow* consistency condition for time-averaged Hamiltonian dynamics. Unlike prior approaches, this allows training on independent phase-space samples without access to future states, avoiding expensive trajectory generation. Validated across diverse Hamiltonian systems, our method in particular improves upon molecular dynamics simulations using machine-learned force fields (MLFF). Our models maintain comparable training and inference cost, but support significantly larger integration timesteps while trained directly on widely-available *trajectory-free* MLFF datasets.

Applications · Chemistry, Physics, and Earth Sciences

Orestis Oikonomou, Levi Lingsch, Dana Grund, Siddhartha Mishra, Georgios Kissas

Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search in combinatorial spaces. We introduce SIGS, a neuro-symbolic framework that automates this process. SIGS uses a formal grammar to generate only syntactically valid building blocks, embeds these expressions into a continuous space, and then searches this space to assemble, score, and refine candidate closed-form solutions by minimizing a physics-based residual. This design unifies symbolic reasoning with numerical optimization; the grammar constrains candidate solution blocks to be proper by construction, while the latent search makes exploration tractable and data-free. SIGS is the first neuro-symbolic method to (i) analytically solve coupled systems of nonlinear PDEs, (ii) discover solutions under grammar misspecification, and (iii) produce accurate symbolic approximations for PDEs lacking known closed-form solutions. Overall, SIGS achieves orders-of-magnitude improvements in accuracy and efficiency over existing symbolic methods on standard benchmarks.

Applications · Chemistry, Physics, and Earth Sciences

Jannis Becktepe, Aleksandra Franz, Nils Thuerey, Sebastian Peitz

Reinforcement learning (RL) has shown promising results in active flow control (AFC), yet progress in the field remains difficult to assess as existing studies rely on heterogeneous observation and actuation schemes, numerical setups, and evaluation protocols. Current AFC benchmarks attempt to address these issues but heavily rely on external computational fluid dynamics (CFD) solvers, are not fully differentiable, and provide limited 3D and multi-agent support. To overcome these limitations, we introduce FluidGym, the first standalone, fully differentiable benchmark suite for RL in AFC. Built entirely in PyTorch on top of the GPU-accelerated PICT solver, FluidGym runs in a single Python stack, requires no external CFD software, and provides standardized evaluation protocols. We present baseline results with PPO and SAC and release all environments, datasets, and trained models as public resources. FluidGym enables systematic comparison of control methods, establishes a scalable foundation for future research in learning-based flow control, and is available at https://anonymous.4open.science/r/fluidgym (anonymized mirror of our public repository).

Applications · Chemistry, Physics, and Earth Sciences

Karen Sargsyan, Chao-Ping Hsu

Finding exact solutions to the quantum many-body problem is computationally intractable (QMA-hard). Traditional approximations for electrons in an atom or molecule---density functional theory and wavefunction methods---have been indispensable, but their development shows signs of saturation: DFT functionals have proliferated without converging toward the exact functional, and strong correlation remains largely unsolved after decades of effort. This position paper argues that machine learning represents the most promising path forward---not as a proof of logical necessity, but as a decision-theoretic argument: ML succeeds whether the underlying problems are truly hard or merely lack simple analytical solutions. We reframe recent traditional method development as ``hand-crafted machine learning'' that has exhausted the hypothesis space accessible to human intuition. Significant challenges remain, but these have clear research paths forward, unlike the fundamental barriers facing traditional approaches. ML-based approaches merit strategic priority in quantum chemistry's next phase.

Applications · Chemistry, Physics, and Earth Sciences

Dario Coscia, Pim de Haan, Max Welling

Machine Learning Interatomic Potentials (MLIPs) are becoming a central tool in simulation-based chemistry. However, like most deep learning models, MLIPs struggle to make accurate predictions on out-of-distribution data or when trained in a data-scarce regime, both common scenarios in simulation-based chemistry. Moreover, MLIPs do not provide uncertainty estimates by construction, which are fundamental to guide active learning pipelines and to ensure the accuracy of simulation results compared to quantum calculations. To address this shortcoming, we propose BLIPs: Bayesian Learned Interatomic Potentials. BLIP is a scalable, architecture-agnostic variational Bayesian framework for training or fine-tuning MLIPs, built on an adaptive version of Variational Dropout. BLIP delivers well-calibrated uncertainty estimates and minimal computational overhead for energy and forces prediction at inference time, while integrating seamlessly with (equivariant) message-passing architectures. Empirical results on simulation-based computational chemistry tasks demonstrate improved predictive accuracy with respect to standard MLIPs, and trustworthy uncertainty estimates, especially in data-scarse or heavy out-of-distribution regimes. Moreover, fine-tuning pretrained MLIPs with BLIP yields consistent performance gains and calibrated uncertainties.

Applications · Chemistry, Physics, and Earth Sciences

Vincent Guan, Lazar Atanackovic, Kirill Neklyudov

The population dynamics of molecules, cells, and organisms are governed by a number of unknown internal and external forces. In the last decade, population dynamics have predominately been modeled with Wasserstein gradient flows. However, since gradient flows minimize free energy, they fail to capture important dynamical properties, such as periodicity. In this work, we propose a change in perspective by considering population dynamics that minimize Wasserstein Lagrangian action, rather than free energy. As our main theoretical contributions, we derive the Hamiltonian equations of motion from the principle of least population-level action and we show that these mechanics encompass classical mechanics, quantum mechanics, and gradient flows. We further leverage the Hamiltonian perspective to propose an algorithm that learns the population mechanics from observed marginals, without specifying the Lagrangian. We demonstrate that by directly learning the population mechanics, our method forecasts and interpolates unseen marginals without a reference process, and outperforms gradient flow and flow matching methods across a wide range of real and simulated experiments.

Applications · Chemistry, Physics, and Earth Sciences

Cheng Jing, Uvini Mudiyanselage, Woojin Cho, Minju Jo, Anthony Gruber, Kookjin Lee

Structure-preserving approaches to dynamics discovery have demonstrated great potential for modeling physical systems due to their use of strong inductive biases, which enforce key features such as conservation laws and dissipative behavior. However, these models are typically trained on a per-configuration basis, requiring explicit knowledge of system parameters and costly retraining when these parameters vary. While meta-learning provides a potential remedy, optimization-based approaches can suffer from limited generalizability. Motivated by recent advances in modulation-based learning aimed at mitigating these drawbacks, we systematically investigate the use of modulation techniques in learning conservative dynamical systems. We study a range of existing modulation strategies alongside newly proposed variants, integrating them into a Hamiltonian learning framework without requiring an explicit system parameterization. Through extensive experiments on benchmark problems, we demonstrate that modulation-based meta-learning enables accurate few-shot adaptation, achieving robust generalization across parameter space without compromising the conservation of key invariants responsible for the dynamics.