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Applications · Chemistry, Physics, and Earth Sciences

Zhonghao Li, Chaoyu Liu, Qian Zhang

Partial differential equations (PDEs) are fundamental for modeling complex natural and physical phenomena. In many real-world applications, however, observational data are \textbf{extremely sparse}, which severely limits the applicability of both classical numerical solvers and existing neural approaches. While neural methods have shown promising results under moderately sparse observations, their inference efficiency at high resolutions is limited, and their accuracy degrades substantially in the extremely sparse regime. In this work, we propose the \textbf{Di-BiLPS}, a unified neural framework that effectively handle \textbf{both forward and inverse} PDE problems under extremely sparse observations. Di-BiLPS combines a variational autoencoder to compress high-dimensional inputs into a compact latent space, a latent diffusion module to model uncertainty, and contrastive learning to align representations. Operating entirely in this latent space, the framework achieves efficient inference while retaining flexible input–output mapping. In addition, we introduce a \textbf{PDE-informed denoising algorithm} based on a variance-preserving diffusion process, which further improves inference efficiency. Extensive experiments on multiple PDE benchmarks demonstrate that Di-BiLPS consistently achieves \textbf{SOTA performance under extremely sparse inputs (as low as 3\%)}, while substantially reducing computational cost. Moreover, Di-BiLPS enables \textbf{zero-shot super-resolution}, as it allows predictions over continuous spatial–temporal domains.

Applications · Chemistry, Physics, and Earth Sciences

Philipp Höllmer, Stefano Martiniani

Continuous-time generative models for crystalline materials enable inverse materials design by learning to predict stable crystal structures, but incorporating explicit target properties into the generative process remains challenging. Policy-gradient reinforcement learning (RL) provides a principled mechanism for aligning generative models with downstream objectives but typically requires access to the score, which has prevented its application to flow-based models that learn only velocity fields. We introduce Open Materials Generation with Inference-time Reinforcement Learning (OMatG-IRL), a policy-gradient RL framework that operates directly on the learned velocity fields and eliminates the need for the explicit computation of the score. OMatG-IRL leverages stochastic perturbations of the underlying generation dynamics preserving the baseline performance of the pretrained generative model while enabling exploration and policy-gradient estimation at inference time. Using OMatG-IRL, we present the first application of RL to crystal structure prediction (CSP). Our method enables effective reinforcement of an energy-based objective while preserving diversity through composition conditioning, and it achieves performance competitive with score-based RL approaches. Finally, we show that OMatG-IRL can learn time-dependent velocity-annealing schedules, enabling accurate CSP with order-of-magnitude improvements in sampling efficiency and, correspondingly, reduction in generation time.

Applications · Chemistry, Physics, and Earth Sciences

Zhang Yiyuan, Cailong Hua, Vinitendra Singh, Joseph Muretta, James Ervasti, Murti Salapaka

Many fundamental biological processes are governed by mechanical forces, with proteins acting as the key molecular mediators. Elucidating how protein unfolding responds to force is critical for understanding the mechano-pathologies, such as cardiomyopathy and muscular dystrophy. While the unfolding trajectories measured by Single-Molecule Force Spectroscopy (SMFS) map the instantaneous force response against molecular extension, its broader application is limited by time-consuming data collection and high operational costs. Here, we present the first scalable generative diffusion framework for full unfolding trajectory prediction, which integrates protein encoders for multi-scale conditioning. Beyond establishing the field's first systematic benchmark using existing models, we propose GenUnfold, a novel physics-guided diffusion model that combines global coevolutionary context with a local mechanical representation of the protein. The representation is derived from a novel physics-biased attention mechanism, which steers the generative diffusion process by modeling dynamic residue dependencies as a function of both structural topology and interaction stiffness. The benchmark for this task is built upon the biomolecule stretching database and several representative baseline models. Empirical results demonstrate that GenUnfold achieves state-of-the-art performance, reducing distributional error (FID) by 30\% and 54\% compared to pretrained Evolutionary Scale Model (ESM)-2 and standard transformer, respectively. Beyond statistical curve similarity, GenUnfold demonstrates superior physical consistency; in downstream mechanical property prediction, it reduces prediction errors for unfolding force and energy distributions by 6\% and 36\% over the ESM-2 baseline. These results indicate that while existing generative AI approaches can alleviate the need for predicting representative force curves, GenUnfold further improves performance by leveraging the synergy between protein structure and evolutionary information. By enabling proteome-wide screening to identify mechanical candidates before costly physical validation, our approach is promising to accelerate the discovery of force-targeted therapeutics.

Applications · Chemistry, Physics, and Earth Sciences

Montgomery Bohde, Hongxuan Liu, Mrunali Manjrekar, Magdalena Lederbauer, Shuiwang Ji, Runzhong Wang, Connor Coley

Tandem mass spectrometry is prominent in scientific discovery workflows for identifying unknown small molecules, yet high-throughput structural elucidation remains challenging. While recent autoregressive and graph diffusion models have shown promise in *de novo* elucidation, performance remains limited by poor scalability during both training and inference time. In this work, we present FRIGID, a framework with a novel diffusion language model that generates molecular structures conditioned on mass spectra via intermediate fingerprint representations and determined chemical formulae, training at the scale of hundreds of millions of unlabeled structures. We then demonstrate how forward fragmentation models enable inference-time scaling by identifying spectrum-inconsistent fragments and refining them through targeted remasking and denoising. While FRIGID already achieves strong performance with its diffusion base, inference-time scaling significantly improves its accuracy, surpassing 15% Top-1 accuracy on the challenging MassSpecGym benchmark and more than doubling the Top-1 accuracy of the leading methods on NPLIB1. Further empirical analyses show that FRIGID exhibits log-linear performance scaling with increasing inference-time compute, opening a promising new direction for continued improvements in *de novo* structural elucidation.

Applications · Chemistry, Physics, and Earth Sciences

Muhammad Umer Sheikh, Hassan Abid, Khawar shehzad, Ufaq Khan, Muhammad Haris Khan

Climate change research increasingly requires AI systems that reason across text, dynamic visual content, and scientific figures, yet existing climate QA benchmarks are small, mostly textual, and cover a narrow range of models. We introduce MMClima, a large-scale multimodal climate question answering framework with over 104k expert-validated question–answer pairs spanning articles, video transcriptions, and figures across five core climate science domains. MMClima is constructed via automated claim extraction and QA synthesis with human-in-the-loop validation to ensure both scale and reliability. Using MMClima, we benchmark state-of-the-art multimodal language models on tasks requiring factual recall, visual interpretation, and cross-modal synthesis. We additionally fine-tune on the textual split to produce mmclima-70b-txt, a domain-adapted baseline that outperforms strong open- and closed-source models on textual QA. We release the dataset, evaluation pipeline, fine-tuned model weights, and data creation framework to support standardized multimodal evaluation for climate science.

Applications · Chemistry, Physics, and Earth Sciences

Nicholas Gao, Till Grutschus, Frank Noe, Stephan Günnemann

Neural-network wave functions in Variational Monte Carlo (VMC) have achieved great success in accurately representing both ground and excited states. However, achieving sufficient numerical accuracy of state overlaps requires growing the number of Monte Carlo samples, and consequently computational cost, with the number of states. We present a nearly constant sample size approach named Multi-State Importance Sampling (MSIS), which leverages all states' samples to estimate any pairwise overlap. To efficiently evaluate all states for all samples, we introduce Excited Pfaffians. Inspired by Hartree-Fock, this architecture represents many states within a single neural network. Excited Pfaffians also serve as generalized wave functions, allowing a single model to represent multi-state potential energy surfaces. On the carbon dimer, we match the $\mathcal{O}(N_s^4)$-scaling natural excited states while training $>200\times$ faster and modeling 50% more states. Our favorable scaling enables us to be the first to use neural networks to find all distinct energy levels of the Beryllium atom. Finally, we demonstrate that a single wave function can represent excited states across various molecules.

Applications · Chemistry, Physics, and Earth Sciences

Dexiong Chen, Andrei Manolache, Mathias Niepert, Karsten Borgwardt

Classifying protein topology is essential for deciphering biological function, but progress is held back by the lack of large-scale benchmarks that avoid duplicates and by models that do not scale well. We introduce TEDBench, a large-scale, non-redundant benchmark for protein fold classification constructed from the Encyclopedia of Domains (TED) and Foldseek-clustered AlphaFold structures. We show that on TEDBench, current protein representation learning methods either require very large models or fail to deliver strong performance. To address this challenge, we propose Masked Invariant Autoencoders (MiAE), a self-supervised framework for protein structure representation learning. MiAE uses an extremely high masking ratio of up to 90% with an $\mathrm{SE(3)}$-invariant encoder and a lightweight decoder that reconstructs backbone coordinates from the latent representation and mask tokens. MiAE scales well and outperforms supervised counterparts and state-of-the-art baselines on TEDBench, establishing a strong recipe for protein fold classification. To test transfer beyond AlphaFold structures, we further benchmark on a curated dataset from experimental structures of CATH 4.4. We will release TEDBench and model checkpoints.

Applications · Chemistry, Physics, and Earth Sciences

Yuejiang Yu, Langwen Huang, Alexandru Calotoiu, Torsten Hoefler

Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size ($N$), dataset size ($D$), and compute budget ($C$). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10× reduces validation loss by up to 3.2×. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to longer training durations yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance.\footnote{Code is available at \url{https://anonymous.4open.science/r/scaling-laws-weather-model-8560/}}

Applications · Chemistry, Physics, and Earth Sciences

Xingyue Zhang, Yuxuan Bao, Mars Liyao Gao, J. Nathan Kutz

Bridging the gap between data-rich training regimes and observation-sparse deployment conditions remains a central challenge in spatiotemporal field reconstruction, particularly when target domains exhibit distributional shifts, heterogeneous structure, and multi-scale dynamics absent from available training data. We present SENDAI, a hierarchical $\textbf{S}$parse-measurement, $\textbf{E}$fficie$\textbf{N}$t $\textbf{D}$ata $\textbf{A}$ss$\textbf{I}$milation Framework that reconstructs full spatial states from hyper sparse sensor observations by combining simulation-derived priors with learned discrepancy corrections. We demonstrate the performance on satellite remote sensing, reconstructing MODIS (Moderate Resolution Imaging Spectroradiometer) derived vegetation index fields across six globally distributed sites. Using seasonal periods as a proxy for domain shift, the framework consistently outperforms established baselines that require substantially denser observations---SENDAI achieves a maximum SSIM improvement of 185% over traditional baselines and a 36% improvement over recent high-frequency-based methods. These gains are particularly pronounced for landscapes with sharp boundaries and sub-seasonal dynamics; more importantly, the framework effectively preserves diagnostically relevant structures---such as field topologies, land cover discontinuities, and spatial gradients. By yielding corrections that are more structurally and spectrally separable, the reconstructed fields are better suited for downstream inference of indirectly observed variables. The results therefore highlight a lightweight and operationally viable framework for sparse-measurement reconstruction that is applicable to physically grounded inference, resource-limited deployment, and real-time monitor and control.

Applications · Chemistry, Physics, and Earth Sciences

Zhao Yanshun, Xiaoyu Peng, Congcong Zhu, Jiamin Jiang, Jingrun Chen

Conventional patchified Transformers operate on uniform spatial partitions, distributing computational effort evenly across the domain irrespective of local features. This inflexible tokenization scheme is inherently limited in its ability to efficiently represent and process solutions to complex PDEs. To address this, we propose MeshTok, an adaptive mesh refinement (AMR)-inspired tokenization and sequence modeling framework. This method selectively refines spatial regions exhibiting sharp gradients, transient features, or multiscale structures, generating a heterogeneous set of multiscale tokens defined on a fixed simulation grid. These tokens are processed within a unified Transformer sequence, enabling the model to simultaneously capture coarse-grained global context and fine-grained local details without requiring specialized architectural components. Although adaptive refinement moderately increases token count, it promotes a more targeted allocation of computational resources to physically informative regions, thereby enhancing predictive accuracy under equivalent computational constraints. Experimental evaluations across multiple PDE families and benchmark datasets demonstrate that MeshTok consistently improves the efficiency–accuracy trade-off compared to uniform-grid baselines. This suggests adaptive multiscale tokenization as a scalable and generalizable design principle for neural PDE modeling.

Applications · Chemistry, Physics, and Earth Sciences

Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space-time PINNs take time as an input but reuse a single network with shared weights across all times, forcing the same features to represent markedly different dynamics. This coupling degrades accuracy and can destabilize training when enforcing PDE, boundary, and initial constraints jointly. We propose *Time-Induced Neural Networks (TINNs)*, a novel architecture that parameterizes the network weights as a learned function of time, allowing the effective spatial representation to evolve over time while maintaining shared structure. The resulting formulation naturally yields a nonlinear least-squares problem, which we optimize efficiently using a Levenberg-Marquardt method. Experiments on various time-dependent PDEs show up to $4\times$ improved accuracy and $10\times$ faster convergence compared to PINNs and strong baselines.

Applications · Chemistry, Physics, and Earth Sciences

Yeqiu Chen, Ziyan Liu, Hong Wang, Lei Liu

Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods offer an efficient and parallelizable framework. However, their performance is critically dependent on the selection of \textit{integration contours}---improper selection without reliable prior knowledge of eigenvalue distribution can incur significant computational overhead and compromise numerical accuracy. To address this challenge, we propose **Deepcontour**, a novel hybrid framework that integrates a deep learning-based spectral predictor with Kernel Density Estimation (KDE) for principled contour design. Specifically, Deepcontour utilizes its specialized Eigen-Neural-Operator (ENO) to provide rapid spectral distribution priors, driving a KDE module to automatically construct the optimized integration contours, which guide the CI solver to efficiently find the desired eigenvalues. Deepcontour achieves up to a 5.63x speedup across diverse scientific datasets while maintaining strict numerical rigor. By merging the predictive power of deep learning with the numerical rigor of classical solvers, this work establishes an efficient and robust paradigm for solving large-scale GEPs.

Applications · Chemistry, Physics, and Earth Sciences

Chenhui Xu, Fuxun Yu, Michael Bianco, Jacob Kovarskiy, Raphael Tang, Qi Zhang, Zirui Xu, Will LeVine, Brandon Dubbs, Heming Liao 等

Training robust reasoning vision-language models (VLMs) in rare domains (such as geospatial) is fundamentally constrained by supervision scarcity. While raw geospatial imagery is abundant, the amount of task-direct supervision falls far behind that of common domains. In this work, we validate an important conclusion: indirect verifiable rewards, derived from seemingly unrelated metadata, are sufficient to induce sophisticated and generalizable geospatial reasoning across a wide range of downstream tasks (25+). We present Geo-R1 as one empirical instantiation of this paradigm. Rather than relying on limited task-specific annotations (i.e., direct rewards), Geo-R1 utilizes scalable, verifiable indirect proxy rewards based on cross-view alignment with metadata (geolocation information) to drive reinforcement learning at scale. Such indirect rewards successfully motivate the model to discover and internalize zero-shot geospatial reasoning across diverse tasks, achieving extraordinary zero-shot transfer on out-of-distribution benchmarks and even surpassing fully supervised specialists on certain benchmarks. These findings indicate that optimizing for indirect verifiable rewards may provide a scalable pathway to unlock generalized reasoning capabilities in rare domains with massive unlabeled data archives. Our code is available at: \url{https://anonymous.4open.science/r/Geo-R1-ICML}.

Applications · Chemistry, Physics, and Earth Sciences

Li Sun, Hongbo Lv, Zhikai Jiang, Zhongtian Sun, Lanxu Yang, Philip Yu

Partial Differential Equations (PDEs) play a fundamental role in scientific computing, and recent efforts have sought to extend the success of foundation models to PDE solving. However, multi-physics PDE pre-training faces the unique challenge of disentangling dynamic heterogeneity to learn universal, elementary patterns that generalize to new PDEs. Additionally, cross-physics transfer lacks a theoretical framework for interpretability—specifically, understanding which pre-trained operator knowledge is effectively transferred to target PDEs. To bridge these gaps, we introduce the theory of neural operator splitting, which decomposes PDE evolution into a modulated global spectral operator and sparse local constitutive mechanisms. A key innovation is Origo, which provides a neural operator bank that enables the identification of operator-level generalization patterns. Extensive experiments demonstrate strong zero-shot generalization and mechanism-level interpretability on unseen PDEs.

Applications · Chemistry, Physics, and Earth Sciences

Hwanhee Kim, Seungyeon Choi, Sanghyun Park

Generative Flow Networks (GFlowNets) have emerged as a powerful framework for molecular generation, sampling diverse candidates proportionally to a reward function. However, the vast chemical space necessitates truncating trajectory length, forcing models to treat incomplete molecular fragments as terminal states alongside valid molecules. This conflation distorts the learned distribution by allocating probability mass to chemically meaningless states. We propose LeakGFN, a dual-head architecture that decomposes flow into two components: a chemical head modeling flow over the full chemical space, and a valid head estimating the fraction of flow reaching valid molecules within the truncation boundary. Through this decomposition, the valid head implicitly learns molecular reachability without explicit supervision. We prove that LeakGFN recovers the correct distribution over accessible molecules under mild assumptions. Experiments on five molecular optimization tasks demonstrate consistent improvements over flow matching baselines, achieving state-of-the-art performance on four out of five tasks. Our module integrates as a plug-and-play enhancement into existing frameworks, improving performance on both pocket-conditioned and multi-objective generation tasks.

Applications · Chemistry, Physics, and Earth Sciences

Sepehr Mousavi, Siddhartha Mishra, Laura De Lorenzis

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Sungwoo Park

We introduce Euler–Poincaré Neural Dynamics (EPND), a geometric-mechanics–driven framework that redefines how Koopman-type neural models learn dynamical systems. Unlike conventional operator-learning methods that rely on function-space linearization, EPND places geometric mechanics at the core of its architecture the mathematical engine governing evolution through Lie-group flows. This foundation enables a principled treatment of curvature, symmetry, and conservation, that ensures both interpretability and physical consistency. Building on this foundation, we develop the Euler–Poincaré Parallel Scan, a parallel algorithm that leverages the associative algebra of Lie-group compositions to overcome the inefficiencies of sequential computation. By unifying geometric structure with scalable computation, EPND achieves high accuracy, strong stability, and significant parallel acceleration in modeling long-horizon dynamics of versatile scientific simulation.

Applications · Chemistry, Physics, and Earth Sciences

Jiwoong Kim, Jongwon Lee, Jungwoo Park, Sungwoo Park

We present a Lie-algebraic approach to model Koopman dynamics that integrates algebraic structure with computational scalability. The proposed formulation constrains the neural generators to evolve within prescribed Lie subalgebras and constructs finite-time flows through a neural Magnus expansion construction, thereby maintaining consistency with the associated Lie-group composition over each time segment. To address the computational burden inherent in sequential propagation, we exploit the associativity of Lie-group compositions and construct segmentwise propagators via a prefix-scan algorithm, which reduces the depth of temporal composition from linear to logarithmic. Consequently, the framework enables accurate long-horizon prediction while improving computational efficiency, and provides a principled foundation for scalable Koopman operator learning for nonlinear systems.

Applications · Chemistry, Physics, and Earth Sciences

Jan Hagnberger, Mathias Niepert

Machine learning–based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an additional input, thereby reducing prediction errors. However, generating a simulation mesh for new geometries is computationally costly. In contrast, mesh-free methods, which do not rely on the simulation mesh, typically incur higher errors. Motivated by these considerations, we introduce SMART, a neural surrogate model that predicts physical quantities at arbitrary query locations using only a point-cloud representation of the geometry, without requiring access to the simulation mesh. The geometry and simulation parameters are encoded into a shared latent space that captures both structural and parametric characteristics of the physical field. A physics decoder then attends to the encoder's intermediate latent representations to map spatial queries to physical quantities. Through this cross-layer interaction, the model jointly updates latent geometric features and the evolving physical field. Extensive experiments show that SMART is competitive with and often outperforms existing methods that rely on the simulation mesh as input, demonstrating its capabilities for industry-level simulations.

Applications · Chemistry, Physics, and Earth Sciences

Dian Jin, Yancheng Yuan, Xiaoming Tao

End-to-end prediction of high-order crystal tensor properties from atomic structures remains challenging: while spherical-harmonic equivariant models are expressive, their Clebsch-Gordan tensor products incur substantial compute and memory costs for higher-order targets. We propose the Cartesian Environment Interaction Tensor Network (CEITNet), an approach that constructs a multi-channel Cartesian local environment tensor for each atom and performs flexible many-body mixing via a learnable channel-space interaction. By performing learning in channel space and using Cartesian tensor bases to assemble equivariant outputs, CEITNet enables efficient construction of high-order tensor. Across benchmark datasets for order-2 dielectric, order-3 piezoelectric, and order-4 elastic tensor prediction, CEITNet surpasses prior high-order prediction methods on key accuracy criteria while offering high computational efficiency. Code is provided in supplementary materials.