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Applications · Chemistry, Physics, and Earth Sciences

Zishuo Lan, Junjie Li, Lei Wang, Jincheng Wang

Autoregressive learning of time-stepping operators offers an effective approach to data-driven PDE simulation on grids. For conservation laws, however, long-horizon rollouts are often destabilized when learned updates violate global conservation and, in many applications, additional state bounds—such as nonnegative mass and densities or concentrations constrained to [0,1]. Enforcing these coupled constraints via direct next-state regression remains difficult. We introduce a framework for learning conservative transport operators on regular grids, inspired by lattice Boltzmann–style discrete-velocity transport representations. Instead of predicting the next state, the model outputs local transport operators that update cells through neighborhood exchanges, guaranteeing discrete conservation by construction. For bounded quantities, we parameterize transport within a capacity-constrained feasible set, enforcing bounds structurally rather than by post-hoc clipping. We validate FluxNet on convection-diffusion, shallow water equations, traffic flow, and spinodal decomposition. Experiments on shallow-water equations and traffic flow show improved rollout stability and physical consistency over strong baselines. On phase-field spinodal decomposition, the method enables large time-steps with long-range transport, accelerating simulation while preserving microstructure evolution in both pointwise and statistical measures.

Applications · Chemistry, Physics, and Earth Sciences

Haozhe Jia, Pengyu Yin, Wenshuo Chen, Shaofeng Liang, Lei Wang, Bowen Tian, Xiucheng Wang, Jia Nanqian, Yutao Yue

Physics-informed diffusion models typically impose PDE constraints only on the final output, leaving intermediate features unconstrained. This can enable shortcut solutions that fit training statistics yet generalize poorly under shifted boundary conditions. We introduce \textbf{REPA-P}, a \emph{teacher-free} physics-informed representation alignment framework that uses first-principles residuals as supervision. REPA-P attaches lightweight projection heads to a few early/mid layers of a diffusion backbone, decodes hidden activations into physical states, and applies PDE and boundary-condition residual losses to these intermediate predictions during training. The heads are discarded at inference, preserving the original architecture and sampling cost. Across three 2D scientific field benchmarks (Darcy flow, topology optimization, and Electrostatic Charge Potential), REPA-P accelerates convergence, reduces physics residuals by up to 80\%, and improves out-of-distribution robustness to boundary-condition shifts while maintaining generation quality with zero inference overhead. Ablations show that supervising only a small set of intermediate layers captures most gains and complements output-level physics losses.

Applications · Chemistry, Physics, and Earth Sciences

Yanhui Zhu, Chen Zhao, Yinhao Li, Xiangfu Meng

Current data-driven scientific modeling struggles with a functional dichotomy: neural operators exhibit spectral bias in high-frequency regimes, while physics-constrained paradigms suffer from optimization pathologies. To bridge this gap, we propose Adaptive Physics-Informed Computing (APIC), a neuro-symbolic meta-architecture designed with structural reconfigurability to encode diverse domain priors. Crucially, APIC integrates a gradient-isolated interaction strategy that mechanistically decouples the optimization paths of parameter identification and residual correction, effectively mitigating gradient interference/conflicts. By instantiating this framework for nonlinear dissipative systems, we derive the Generalized Kuramoto-Sivashinsky-Cahn-Hilliard (G-KSCH) kernel, providing a unified representation for sparse dynamic identification. Extensive experiments demonstrate that APIC establishes new benchmarks in 3D compressible supersonic shock wave prediction, surpassing diverse architectures (e.g., CNNs and Transformers) by 20% to 70% in predictive accuracy. Notably, APIC achieves Pareto-optimal performance, delivering superior precision with reduced computational overhead compared to SOTA models, while exhibiting robust cross-domain generalization across meteorological and urban traffic datasets.

Applications · Chemistry, Physics, and Earth Sciences

Taewon Kim, Jihwan Shin, Hyomin Kim, Youngmok Jung, Jonghoon Lee, Won-Chul Lee, Insu Han, Sungsoo Ahn

DNA language models are increasingly used to represent genomic sequence, yet their effectiveness depends critically on how raw nucleotides are converted into model inputs. Unlike natural language, DNA offers no canonical “word” boundaries, making fixed tokenizations a brittle design choice under shifts, indels, and local repeats. We introduce DNAChunker, a masked DNA language model that incorporates a learnable adaptive segmentation module to produce context-dependent, variable-length units. Building on a dynamic segmentation procedure, DNAChunker learns to allocate finer granularity to functionally enriched regions while compressing repetitive or redundant sequence. We pre-train DNAChunker on the human reference genome (HG38) and evaluate it on the Nucleotide Transformer and Genomic Benchmarks, where it consistently improves over strong fixed-tokenization baselines. Further analyses and ablations indicate that the learned segmentation is structured rather than incidental: the model preferentially uses shorter units around promoters and exons, and longer units in repetitive regions, yielding representations that are both mutation-resilient and biologically-informed.

Applications · Chemistry, Physics, and Earth Sciences

Nima Leclerc, Chris Miller, Nicholas Brawand

Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for meta-learning showing that the adaptation gain (expected fidelity improvement from task-specific gradient steps) saturates exponentially with gradient steps and scales linearly with task variance, providing a quantitative criterion for when adaptation justifies its overhead. Validation on quantum gate calibration shows negligible benefits for low-variance tasks but $>40$% fidelity gains on two-qubit gates under extreme out-of-distribution conditions (10$\times$ the training noise), with implications for reducing per-device calibration time on cloud quantum processors. Further validation on classical linear-quadratic control confirms these laws emerge from general optimization geometry rather than quantum-specific physics. Together, these results offer a transferable framework for decision-making in adaptive control.

Applications · Chemistry, Physics, and Earth Sciences

Paul Schwerdtner, Tobias Blickhan, Benjamin Peherstorfer

This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only sampling-time transports from a base distribution to each marginal and then extract a physics-time velocity by regressing on coupled synthetic trajectories. We prove that the resulting physics-time dynamics are unique and inherit regularity from the sampling-time transports. Because we can build on standard, well-developed conditional flow matching techniques for learning the base-to-marginal transports, our approach scales to high dimensions and avoids per-step optimal-transport couplings, while allowing admissible non-gradient dynamics that can naturally explain rotational or circulating physics phenomena.

Applications · Chemistry, Physics, and Earth Sciences

Tianchi Yu, Ivan Oseledets

For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \leq d \lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems ($d\gg 10$), spectral methods suffer from the curse of dimensionality. Physics-informed neural networks (PINNs) have emerged as a promising approach to overcome this challenge, offering scalability to high dimensions, but often suffer from limited accuracy and efficiency. Recently proposed spectral-informed neural networks (SINNs) combine spectral methods with PINNs, operating directly in the spectral domain to avoid spatial derivative computations and to reduce memory consumption. In this work, we introduce Modified SINNs, which integrate coefficient decay scaling and basis embeddings motivated by harmonic analysis to enhance accuracy in high-dimensional problems and enable accurate approximation of unknown spectral coefficients. Numerical experiments on steady and time-dependent partial differential equations demonstrate that Modified SINNs outperform sparse grid spectral methods on middle-dimensional problems with incomplete spectral information and achieve superior accuracy compared to PINNs on high-dimensional problems.

Applications · Chemistry, Physics, and Earth Sciences

Vansh Ramani, Har Ashish Arora, Dhairya Kuchhal, Sayan Ranu, Tarak Karmakar

High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce $Dissolvr$, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that $Dissolvr$ approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.

Applications · Chemistry, Physics, and Earth Sciences

Yingheng Wang, Tao Yu, Shufeng Kong, Yingheng Wang, John Gregoire, Carla Gomes

Structured scientific spectra encode rich physical information while satisfying hard constraints such as conservation and spectral geometry. We study a canonical example, the electronic density of states (eDOS), whose accurate prediction is central to materials discovery. Prior methods often (i) decouple band gaps from eDOS, (ii) violate total-state conservation, or (iii) collapse crystals into global embeddings that obscure atom-projected contributions. We introduce \textbf{DeepSciReasoner}, a design paradigm for deep scientific reasoning under physical constraints. Instantiated for eDOS prediction, DeepSciReasoner combines structure-aware spectrum decoding with constraint-preserving physical reasoning, in this case, mass-conserving iterative refinement. It substantially improves eDOS accuracy while maintaining physical validity, enabling reliable high-throughput screening. Beyond eDOS, DeepSciReasoner offers a reusable blueprint for predicting structured scientific spectra under hard physical constraints.

Applications · Chemistry, Physics, and Earth Sciences

Andy Xu, Rohan Desai, Larry Wang, Ethan Ritz, Gabriel Hope

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a promising approach to improve correctness in LLMs, however, in many scientific problems, the objective is not necessarily to produce \textit{the} correct answer, but instead to produce a diverse array of candidates which satisfy a set of constraints. We study this challenge in the context of materials generation. To this end, we introduce PLaID++, an LLM post-trained for stable and property-guided crystal generation. We find that applying naive preference optimization to a coordinate-based crystal representation leads to mode collapse. Hence, we introduce a compact, symmetry-informed Wyckoff text representation which improves computational efficiency and encourages generalization from physical priors. By encoding symmetry constraints directly into text and guiding model outputs towards desirable chemical space, PLaID++ generates structures that are thermodynamically stable, unique, and novel at a $>$50\% greater rate than prior methods. We further demonstrate that unified training across conditional and unconditional tasks are mutually beneficial in data-sparse regimes. Our work demonstrates the potential of adapting post-training techniques from natural language processing to materials design, paving the way for targeted and efficient discovery of novel materials.

Applications · Chemistry, Physics, and Earth Sciences

Yanming Xia, Angelica Aviles-Rivero

Neural operators perform well on structured domains, yet their behaviour on irregular geometries remains poorly understood. We show that this limitation is not merely an encoding issue, but a depth-wise failure mode inherent to deep operator architectures. We formalise the *Geometric Forgetting Hypothesis*: due to the Markovian structure of operator layers and their reliance on global mixing mechanisms, neural operators progressively lose access to domain geometry as depth increases. Using layer-wise geometric probing, we demonstrate that both spectral and attention-based operators systematically lose geometric fidelity. We show that this geometric forgetting degrades accuracy, stability, and generalisation. To counteract it, we introduce a lightweight *geometry memory injection* mechanism that restores geometric constraints at intermediate depths with minimal architectural overhead. This simple intervention consistently mitigates forgetting and exposes a *geometric shortcut* instability in transformer-based operators, revealing that geometric retention is a structural requirement rather than a design choice.

Applications · Chemistry, Physics, and Earth Sciences

Tianmeng Hu, Biao Luo, Ke Li

Designing RNA sequences that reliably fold into specific secondary structures is essential for understanding their biological functions but remains a challenging computational problem. We propose CocoRNA, a cooperative multi-agent reinforcement learning framework for RNA inverse design. CocoRNA simplifies the design task by decomposing it into smaller sub-problems, each solved collaboratively by multiple agents. This approach reduces the complexity of the problem and improves the exploration of design policies. During training, a centralized critic uses global structural information to guide the agents, enabling them to jointly optimize their design strategies. As a result, CocoRNA learns high-quality RNA design policies that generalize effectively to unseen structures without additional training. Experiments on the Rfam dataset demonstrate that CocoRNA substantially outperforms state-of-the-art methods in both success rate and design speed. Further experiments on other biological sequence design tasks highlight the effectiveness and broad potential of CocoRNA for complex design tasks.

Applications · Chemistry, Physics, and Earth Sciences

Zherui Yang, Haiyang Xin, Tao Du, Ligang Liu

Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying physics. In many PDE regimes, the induced global interaction kernels are empirically compressible, exhibiting rapid spectral decay that admits low-rank approximations. We leverage this observation to unify representative global mixing modules in neural operators under a shared low-rank template: compressing high-dimensional pointwise features into a compact latent space, processing global interactions within it, and reconstructing the global context back to spatial points. Guided by this view, we introduce Low-Rank Spatial Attention (LRSA) as a clean and direct instantiation of this template. Crucially, unlike prior approaches that often rely on non-standard aggregation or normalization modules, LRSA is built purely from standard Transformer primitives, i.e., attention, normalization, and feed-forward networks, yielding a concise block that is straightforward to implement and directly compatible with hardware-optimized kernels. In our experiments, such a simple construction is sufficient to achieve high accuracy, yielding an average error reduction of over 17\% relative to second-best methods, while remaining stable and efficient in mixed-precision training.

Applications · Chemistry, Physics, and Earth Sciences

Alejandro Queiruga, Theo Gutman-Solo, Shuai Jiang

While there are many applications of machine learning (ML) to scientific problems that \emph{look} promising, the eye test can be misleading compared to the quantitative values. Using numerical analysis techniques, we rigorously quantify the accuracy, convergence rates, and generalization bounds of certain ML models applied to linear differential equations (DEs) for parameter discovery or solution finding. Beyond the quantity and discretization of data, we identify that the {function space} of the data is critical to the generalization of the model which can lead to divergence. Similar lack of generalization is empirically demonstrated for commonly used models. Surprisingly, we find that different classes of models can exhibit opposing generalization behaviors. Based on our theoretical analysis, we also introduce a new mechanistic interpretability lens on scientific models whereby Green's function representations can be extracted from the weights of black-box models. Our results inform a new cross-validation technique for measuring generalization in physical systems, and can be useful as a benchmark of future methods.

Applications · Chemistry, Physics, and Earth Sciences

Abdel-Rahim Mezidi, Jordan Patracone, Amaury Habrard

Operator splitting methods are at the foundation of many numerical solvers for partial differential equations. In parallel, unrolled and hybrid learning-based architectures have been introduced to enhance classical solvers, but their design is rarely linked to the underlying problem structure. In this work, we propose a unifying framework that explicitly links operator splitting algorithms from optimization with unrolled hybrid architectures. We show that each operator splitting scheme naturally defines an unrolled architecture, which recovers a wide range of existing plug-and-play and hybrid models as special cases. Using this framework, we design new unrolled hybrid architectures and validate them on benchmark fluid dynamics simulations, where they achieve improved accuracy and stability.

Applications · Chemistry, Physics, and Earth Sciences

Aleix Segui, Wesley Armour

In AI for Science, physics-informed losses are becoming popular to train learned compressors, but their rate-distortion consequences are poorly understood. We formalise this problem via a geometric framework, showing that physics-aware compression is governed by the interaction of two Riemannian structures in latent space: a Hessian-based physics sensitivity geometry induced by the physical observable, and a rate geometry induced by the entropy model. This theoretical view yields an explicit mechanism for error allocation: the codec concentrates precision along spectrally stiff and rate-expensive directions, while pushing uncertainty into directions that are weakly sensed by the physical observable. We prove fundamental limits from this alignment: (i) rate-efficient preservation is theoretically possible only when physical sensitivity is strongly anisotropic, and (ii) when physics and fidelity are not spectrally aligned, improving physical observables at fixed rate provably worsens standard distortion. We validate these predictions across chaotic fluid dynamics simulations, and introduce simple geometric alignment diagnostics that anticipate when physics-aligned training will succeed.

Applications · Chemistry, Physics, and Earth Sciences

Yue Yu, Weiqi Chen, Binqing Wu, Dongliang Cui, Wanyi Jiang, Zongjiang Shang, Bo Wu, Liang Sun, Ling Chen

Accurate seasonal‑to‑interannual climate forecasting provides critical support for decision-making in agriculture, energy, and disaster preparedness. Current deterministic models often fail to capture climate uncertainty, while existing generative approaches oversimplify the system by neglecting key spatiotemporal dependencies and cross-scale interactions. To address these limitations, we introduce ClimateAR, an AutoRegressive generative model for probabilistic seasonal-to-interannual Climate forecasting. The framework incorporates two novel components: (1) an aligned tokenizer that bridges and aligns heterogeneous simulation and real-world data to improve transferability across domains, and (2) a mixed-scale conditioning mechanism that captures multi-scale climate interactions for robust probabilistic forecasting. Extensive evaluations on the ERA5 reanalysis dataset show that ClimateAR achieves state-of-the-art performance, improving anomaly correlation skill by 37.56\% on average compared to leading baselines. The Code is available at https://anonymous.4open.science/r/ClimateAR-956D.

Applications · Chemistry, Physics, and Earth Sciences

Zhuo Chen, Xinzhe Yuan, Jianshu Zhang, Jinzong Dong, Ruichen Zhou, Yingchun Niu, Tianhang Zhou, Yu Yang Fredrik Liu, Yuqiang Li, Nanyang Ye 等

The high cost and data scarcity in scientific exploration have motivated the use of large language models (LLMs) as knowledge-driven components in Bayesian optimization (BO). However, existing approaches typically embed LLMs directly into the sampling or surrogate modeling pipeline, without fully leveraging their significantly lower evaluation cost compared to real-world experiments. To address this limitation, we propose LLM-Accelerated Bayesian Optimization (LABO), a framework that combines LLM predictions with experimental observations within a single BO loop. LABO employs a gating mechanism to dynamically balance reliance on LLM predictions versus actual experiments. By leveraging inexpensive LLM evaluations to broadly explore the search space and reserving costly real experiments only for regions with high uncertainty, LABO achieves more sample-efficient optimization. We provide a theoretical analysis with a cumulative regret bound that formalizes this efficiency gain. Empirical results across diverse scientific tasks demonstrate that LABO consistently outperforms existing methods under identical experimental budgets. Our results suggest that LABO offers a practical and theoretically grounded approach for integrating LLMs into scientific discovery workflows.

Applications · Chemistry, Physics, and Earth Sciences

Junda Ying, Yuxuan Wang, Bowen Yang, Peijie Zhou, Lei Zhang

Inferring cellular trajectories from destructive snapshots is complicated by the challenges of stochasticity and non-conservative mass dynamics such as cell proliferation and apoptosis. Existing unbalanced Optimal Transport (OT) methods treat mass as a continuous fluid, performing inference at the population level. However, this macroscopic view often fails to capture the discrete, jump-like nature of birth-death events at single-cell resolution, which is essential for understanding lineage branching and fate decisions. We present **Unbalanced Schrödinger Bridge (USB)**, a simulation-free framework for learning underlying dynamics that effectively integrates both stochastic and unbalanced effects which also models the discrete, jump-like birth–death dynamics at single-cell resolution. Theoretically, USB provides a tractable solution to the Branching Schrödinger Bridge (BSB) problem, offering a rigorous microscopic interpretation where individual cells undergo both Brownian motion and discrete birth-death jumps. Technically, the method implements an efficient solver by introducing a simulation-free training objective that effectively scales to high-dimensional omics data. Empirically, we demonstrate on both simulated and real-world datasets that USB not only achieves trajectory reconstruction performance better than or comparable to deterministic baselines but also uniquely enables realistic discrete simulation of birth-death dynamics at single-cell resolution.

Applications · Chemistry, Physics, and Earth Sciences

Wentao Gao, Jiuyong Li, Lin Liu, Thuc Le, Jixue Liu, Yanchang Zhao, Yun Chen

Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through a single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured multi-scale reasoning for climate forecasting without parameter modification. Our approach combines hierarchical coarse-to-fine prediction refinement with residual-guided error correction; together, they systematically address prediction failures at each resolution level. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR consistently enhances foundation model performance across diverse climate regions within an Australian regional area. Experimental results demonstrate substantial improvements over direct foundation model application, achieving up to 18.9\% reduction in mean squared error, 10.2\% reduction in root mean squared error, and 21.1\% relative gain in $R^2$ when applied to TimesFM, with the largest benefits observed in climatologically complex regions where multi-scale temporal dynamics are most pronounced. The framework's inference-time operation enables immediate deployment on existing operational climate prediction systems without model retraining, offering a practical solution for enhancing foundation model capabilities in specialized forecasting domains.