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Applications · Chemistry, Physics, and Earth Sciences

Shilong Tao, Zhe Feng, Haonan Sun, Zhanxing Zhu, Yunhuai Liu

Multi-solid systems are foundational to a wide range of real-world applications, yet modeling their complex interactions remains challenging. Existing deep learning methods predominantly rely on implicit modeling, where the factors influencing solid deformation are not explicitly represented but are instead indirectly learned. However, as the number of solids increases, these methods struggle to accurately capture intricate physical interactions. In this paper, we introduce a novel explicit modeling paradigm that incorporates factors influencing solid deformation through structured modules. Specifically, we present Unisoma, a unified and flexible Transformer-based model capable of handling variable numbers of solids. Unisoma directly captures physical interactions using contact modules and adaptive interaction allocation mechanism, and learns the deformation through a triplet relationship. Compared to implicit modeling techniques, explicit modeling is more well-suited for multi-solid systems with diverse coupling patterns, as it enables detailed treatment of each solid while preventing information blending and confusion. Experimentally, Unisoma achieves consistent state-of-the-art performance across seven well-established datasets and two complex multi-solid tasks. Code is avaiable at [https://github.com/therontau0054/Unisoma](https://github.com/therontau0054/Unisoma).

Applications · Chemistry, Physics, and Earth Sciences

Zelin Xu, Yupu Zhang, Tingsong Xiao, Maitane Lizaso, Jose Gonzalez-Ondina, Zibo Liu, Shigang Chen, Zhe Jiang

Over 40\% of the global population lives within 100 kilometers of the coast, which contributes more than \$8 trillion annually to the global economy. Unfortunately, coastal ecosystems are increasingly vulnerable to more frequent and intense extreme weather events and rising sea levels. Coastal scientists use numerical models to simulate complex physical processes, but these models are often slow and expensive. In recent years, deep learning has become a promising alternative to reduce the cost of numerical models. However, progress has been hindered by the lack of a large-scale, high-resolution coastal simulation dataset to train and validate deep learning models. Existing studies often focus on relatively small datasets and simple processes. To fill this gap, we introduce a decade-long, high-resolution (<100m) coastal circulation modeling dataset on a real-world 3D mesh in southwest Florida with around 6 million cells. The dataset contains key oceanography variables (e.g., current velocities, free surface level, temperature, salinity) alongside external atmospheric and river forcings. We evaluated a customized Vision Transformer model that takes initial and boundary conditions and external forcings and predicts ocean variables at varying lead times. The dataset provides an opportunity to benchmark novel deep learning models for high-resolution coastal simulations (e.g., physics-informed machine learning, neural operator learning).The code and dataset can be accessed at https://github.com/spatialdatasciencegroup/CoastalBench.

Applications · Chemistry, Physics, and Earth Sciences

Chen Wang, Siyu Hu, Guangming Tan, Weile Jia

Pre-trained interatomic potentials have become a new paradigm for atomistic materials simulations, enabling accurate and efficient predictions across diverse chemical systems. Despite their promise, fine-tuning is often required for complex tasks to achieve high accuracy. Traditional parameter-efficient fine-tuning approaches are effective in NLP and CV. However, when applied to SO(3) equivariant pre-trained interatomic potentials, these methods will inevitably break equivariance—a critical property for preserving physical symmetries. In this paper, we introduce ELoRA (Equivariant Low-Rank Adaptation), a novel fine-tuning method designed specifically for SO(3) equivariant Graph Neural Networks (GNNs), the backbones in multiple pre-trained interatomic potentials. ELoRA adopts a path-dependent decomposition for weights updating which offers two key advantages: (1) it preserves SO(3) equivariance throughout the fine-tuning process, ensuring physically consistent predictions, and (2) it leverages low-rank adaptations to significantly improve data efficiency. We prove that ELoRA maintains equivariance and demonstrate its effectiveness through comprehensive experiments. On the rMD17 organic dataset, ELoRA achieves a 25.5\% improvement in energy prediction accuracy and a 23.7\% improvement in force prediction accuracy compared to full-parameter fine-tuning. Similarly, across 10 inorganic datasets, ELoRA achieves average improvements of 12.3\% and 14.4\% in energy and force predictions, respectively. Code will be made publicly available at https://github.com/hyjwpk/ELoRA.

Applications · Chemistry, Physics, and Earth Sciences

Da Long, Zhitong Xu, Guang Yang, Akil Narayan, Shandian Zhe

Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification --- an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.

Applications · Chemistry, Physics, and Earth Sciences

Jinho Chang, Jong Chul YE

With the emergence of diffusion models as a frontline generative model, many researchers have proposed molecule generation techniques with conditional diffusion models. However, the unavoidable discreteness of a molecule makes it difficult for a diffusion model to connect raw data with highly complex conditions like natural language. To address this, here we present a novel latent diffusion model dubbed LDMol for text-conditioned molecule generation. By recognizing that the suitable latent space design is the key to the diffusion model performance, we employ a contrastive learning strategy to extract novel feature space from text data that embeds the unique characteristics of the molecule structure. Experiments show that LDMol outperforms the existing autoregressive baselines on the text-to-molecule generation benchmark, being one of the first diffusion models that outperforms autoregressive models in textual data generation with a better choice of the latent domain.Furthermore, we show that LDMol can be applied to downstream tasks such as molecule-to-text retrieval and text-guided molecule editing, demonstrating its versatility as a diffusion model.

Applications · Chemistry, Physics, and Earth Sciences

Jiao Huang, Qianli Xing, Jinglong Ji, Bo Yang

Graph neural networks have recently demonstrated remarkable performance in predicting material properties. Crystalline material data is manually encoded into graph representations.Existing methods incorporate different attributes into constructing representations to satisfy the constraints arising from symmetries of material structure.However, existing methods for obtaining graph representations are specific to certain constraints, which are ineffective when facing new constraints.In this work, we propose a code generation framework with multiple large language model agents to obtain representations named Rep-CodeGen with three iterative stages simulating an evolutionary algorithm. To the best of our knowledge, Rep-CodeGen is the first framework for automatically generating code to obtain representations that can be used when facing new constraints. Furthermore, a type of representation from generated codes by our framework satisfies six constraints, with codes satisfying three constraints as bases. Extensive experiments on two real-world material datasets show that a property prediction method based on such a graph representation achieves state-of-the-art performance in material property prediction tasks.

Applications · Chemistry, Physics, and Earth Sciences

Guancheng Wan, Zijie Huang, Wanjia Zhao, Xiao Luo, Yizhou Sun, Wei Wang

Coupled dynamical systems govern essential phenomena across physics, biology, and engineering, where components interact through complex dependencies. While Graph Ordinary Differential Equations (GraphODE) offer a powerful framework to model these systems, their **generalization** capabilities degrade severely under limited observational training data due to two fundamental flaws: (i) the entanglement of static attributes and dynamic states in the initialization process, and (ii) the reliance on context-specific coupling patterns during training, which hinders performance in unseen scenarios. In this paper, we propose a Generalizable GraphODE with disentanglement and regularization (GREAT) to address these challenges. Through systematic analysis via the Structural Causal Model, we identify backdoor paths that undermine generalization and design two key modules to mitigate their effects. The *Dynamic-Static Equilibrium Decoupler (DyStaED)* disentangles static and dynamic states via orthogonal subspace projections, ensuring robust initialization. Furthermore, the *Causal Mediation for Coupled Dynamics (CMCD)* employs variational inference to estimate latent causal factors, reducing spurious correlations and enhancing universal coupling dynamics. Extensive experiments across diverse dynamical systems demonstrate that ours outperforms state-of-the-art methods within both in-distribution and out-of-distribution.

Applications · Chemistry, Physics, and Earth Sciences

Jan Pauls, Max Zimmer, Berkant Turan, Sassan Saatchi, Philippe CIAIS, Sebastian Pokutta, Fabian Gieseke

With the rise in global greenhouse gas emissions, accurate large-scale tree canopy height maps are essential for understanding forest structure, estimating above-ground biomass, and monitoring ecological disruptions. To this end, we present a novel approach to generate large-scale, high-resolution canopy height maps over time. Our model accurately predicts canopy height over multiple years given Sentinel 2 time series satellite data. Using GEDI LiDAR data as the ground truth for training the model, we present the first 10 m resolution temporal canopy height map of the European continent for the period 2019–2022. As part of this product, we also offer a detailed canopy height map for 2020, providing more precise estimates than previous studies. Our pipeline and the resulting temporal height map are publicly available, enabling comprehensive large-scale monitoring of forests and, hence, facilitating future research and ecological analyses. For an interactive viewer, see https://europetreemap.projects.earthengine.app/view/europeheight.

Applications · Chemistry, Physics, and Earth Sciences

Shi Yin, Xinyang Pan, fengyan wang, Lixin He

We propose a framework to combine strong non-linear expressiveness with strict SO(3)-equivariance in prediction of the electronic-structure Hamiltonian, by exploring the mathematical relationships between SO(3)-invariant and SO(3)-equivariant quantities and their representations. The proposed framework, called **TraceGrad**, first constructs theoretical SO(3)-invariant **trace** quantities derived from the Hamiltonian targets, and use these invariant quantities as supervisory labels to guide the learning of high-quality SO(3)-invariant features. Given that SO(3)-invariance is preserved under non-linear operations, the learning of invariant features can extensively utilize non-linear mappings, thereby fully capturing the non-linear patterns inherent in physical systems. Building on this, we propose a **grad**ient-based mechanism to induce SO(3)-equivariant encodings of various degrees from the learned SO(3)-invariant features. This mechanism can incorporate powerful non-linear expressive capabilities into SO(3)-equivariant features with correspondence of physical dimensions to the regression targets, while theoretically preserving equivariant properties, establishing a strong foundation for predicting electronic-structure Hamiltonian. Experimental results on eight challenging benchmark databases demonstrate that our method achieves state-of-the-art performance in Hamiltonian prediction.

Applications · Chemistry, Physics, and Earth Sciences

Viacheslav Meshchaninov, Pavel Strashnov, Andrey Shevtsov, Fedor Nikolaev, Nikita Ivanisenko, Olga Kardymon, Dmitry Vetrov

Protein *sequence* design has seen significant advances through discrete diffusion and autoregressive approaches, yet the potential of continuous diffusion remains underexplored. Here, we present *DiMA*, a latent diffusion framework that operates on protein language model representations. Through systematic exploration of architectural choices and diffusion components, we develop a robust methodology that generalizes across multiple protein encoders ranging from 8M to 3B parameters. We demonstrate that our framework achieves consistently high performance across sequence-only (ESM-2, ESMc), dual-decodable (CHEAP), and multimodal (SaProt) representations using the same architecture and training approach. We conduct extensive evaluation of existing methods alongside *DiMA* using multiple metrics across two protein modalities, covering quality, diversity, novelty, and distribution matching of generated proteins. *DiMA* consistently produces novel, high-quality and diverse protein sequences and achieves strong results compared to baselines such as autoregressive, discrete diffusion and flow matching language models. The model demonstrates versatile functionality, supporting conditional generation tasks including protein family-generation, motif scaffolding and infilling, and fold-specific sequence design, despite being trained solely on sequence data. This work provides a universal continuous diffusion framework for protein sequence generation, offering both architectural insights and practical applicability across various protein design scenarios. Code is released at [GitHub](https://github.com/MeshchaninovViacheslav/DiMA).

Applications · Chemistry, Physics, and Earth Sciences

Yeyun Chen

Predicting the solvation free energy of molecules using graph neural networks holds significant potential for advancing drug discovery and the design of novel materials. While previous methods have demonstrated success on independent and identically distributed (IID) datasets, their performance in out-of-distribution (OOD) scenarios remains largely unexplored. We propose a novel Relational Invariant Learning framework (RILOOD) to enhance OOD generalization in solvation free energy prediction. RILOOD comprises three key components: (i) a mixup-based conditional modeling module that integrates diverse environments, (ii) a novel multi-granularity refinement strategy that extends beyond core substructures to enable context-aware representation learning for capturing multi-level interactions, and (iii) an invariant learning mechanism that identifies robust patterns generalizable to unseen environments. Extensive experiments demonstrate that RILOOD significantly outperforms state-of-the-art methods across various distribution shifts, highlighting its effectiveness in improving solvation free energy prediction under diverse conditions.

Applications · Chemistry, Physics, and Earth Sciences

Mohit Pandey, Gopeshh Subbaraj, Artem Cherkasov, Martin Ester, Emmanuel Bengio

Generative Flow Networks (GFlowNets) have recently emerged as a suitable framework for generating diverse and high-quality molecular structures by learning from rewards treated as unnormalized distributions. Previous works in this framework often restrict exploration by using predefined molecular fragments as building blocks, limiting the chemical space that can be accessed. In this work, we introduce Atomic GFlowNets (A-GFNs), a foundational generative model leveraging individual atoms as building blocks to explore drug-like chemical space more comprehensively. We propose an unsupervised pre-training approach using drug-like molecule datasets, which teaches A-GFNs about inexpensive yet informative molecular descriptors such as drug-likeliness, topological polar surface area, and synthetic accessibility scores. These properties serve as proxy rewards, guiding A-GFNs towards regions of chemical space that exhibit desirable pharmacological properties. We further implement a goal-conditioned finetuning process, which adapts A-GFNs to optimize for specific target properties. In this work, we pretrain A-GFN on a subset of ZINC dataset, and by employing robust evaluation metrics we show the effectiveness of our approach when compared to other relevant baseline methods for a wide range of drug design tasks. The code is accessible at https://github.com/diamondspark/AGFN.

Applications · Chemistry, Physics, and Earth Sciences

Cheng-Yen Hsieh, Xinyou Wang, Daiheng Zhang, Dongyu Xue, Fei YE, Shujian Huang, Zaixiang Zheng, Quanquan Gu

Multimodal protein language models (PLMs) integrate sequence and token-based structural information, serving as a powerful foundation for protein modeling, generation, and design. However, the reliance on tokenizing 3D structures into discrete tokens causes substantial loss of fidelity about fine-grained structural details and correlations. In this paper, we systematically elucidate the design space of multimodal PLMs to overcome their limitations. We identify tokenization loss and inaccurate structure token predictions by the PLMs as major bottlenecks.To address these, our proposed design space covers improved generative modeling, structure-aware architectures and representation learning, and data exploration. Our advancements approach finer-grained supervision, demonstrating that token-based multimodal PLMs can achieve robust structural modeling.The effective design methods dramatically improve the structure generation diversity, and notably, folding abilities of our 650M model by reducing the RMSD from 5.52 to 2.36 on PDB testset, even outperforming 3B baselines and on par with the specialized folding models.Project page and code: https://bytedance.github.io/dplm/dplm-2.1.

Applications · Chemistry, Physics, and Earth Sciences

Krzysztof Kacprzyk, Julianna Piskorz, Mihaela van der Schaar

While black-box approaches are commonly used for data-driven modeling of dynamical systems, they often obscure a system's underlying behavior and properties, limiting adoption in areas such as medicine and pharmacology. A two-step process of discovering ordinary differential equations (ODEs) and their subsequent mathematical analysis can yield insights into the system's dynamics. However, this analysis may be infeasible for complex equations, and refining the ODE to meet certain behavioral requirements can be challenging. Direct semantic modeling has recently been proposed to address these issues by predicting the system's behavior, such as the trajectory's shape, directly from data, bypassing post-hoc mathematical analysis. In this work, we extend the original instantiation, limited to one-dimensional trajectories and inputs, to accommodate multi-dimensional trajectories with additional personalization, allowing evolution to depend on auxiliary static features (e.g., patient covariates). In a series of experiments, we show how our approach enables practitioners to integrate prior knowledge, understand the dynamics, ensure desired behaviors, and revise the model when necessary.

Applications · Chemistry, Physics, and Earth Sciences

Jan Ole Ernst, Aniket Chatterjee, Tim Franzmeyer, Axel Kuhn

Quantum control is concerned with the realisation of desired dynamics in quantum systems, serving as a linchpin for advancing quantum technologies and fundamental research. Analytic approaches and standard optimisation algorithms do not yield satisfactory solutions for more complex quantum systems, and especially not for real world quantum systems which are open and noisy. We devise a physics-constrained Reinforcement Learning (RL) algorithm that restricts the space of possible solutions.We incorporate priors about the desired time scales of the quantum state dynamics - as well as realistic control signal limitations - as constraints to the RL algorithm. These constraints improve solution quality and enhance computational scaleability. We evaluate our method on three broadly relevant quantum systems and incorporate real-world complications, arising from dissipation and control signal perturbations. We achieve both higher fidelities - which exceed 0.999 across all systems - and better robustness to time-dependent perturbations and experimental imperfections than previous methods. Lastly, we demonstrate that incorporating multi-step feedback can yield solutions robust even to strong perturbations. Our implementation can be found at: https://github.com/jan-o-e/RL4qcWpc.

Applications · Chemistry, Physics, and Earth Sciences

Jeet Mohapatra, Nima Dehmamy, Csaba Both, Subhro Das, Tommi Jaakkola

We introduce a novel approach for discovering effective degrees of freedom (DOF) in molecular dynamics simulations by mapping the DOF to approximate symmetries of the energy landscape. Unlike most existing methods, we do not require trajectory data but instead rely on knowledge of the forcefield (energy function) around the initial state. We present a scalable symmetry loss function compatible with existing force-field frameworks and a Hessian-based method efficient for smaller systems. Our approach enables systematic exploration of conformational space by connecting structural dynamics to energy landscape symmetries. We apply our method to two systems, Alanine dipeptide and Chignolin, recovering their known important conformations. Our approach can prove useful for efficient exploration in molecular simulations with potential applications in protein folding and drug discovery.

Applications · Chemistry, Physics, and Earth Sciences

Angxiao Yue, Zichong Wang, Hongteng Xu

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications.Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency.In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format.We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves on-par performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37$\times$ faster than RFDiffusion and 63$\times$ faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency.

Applications · Chemistry, Physics, and Earth Sciences

Shu Wei, Yanjie Li, Lina Yu, Weijun Li, Min Wu, Linjun Sun, Jingyi Liu, Hong Qin, Deng Yusong, Jufeng Han 等

The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise.Machine learning methods like genetic algorithms have shown promise in this domain, but are hindered by significant computational time and the complexity of their derived solutions. This paper introduces **SSDE** (Symbolic Solver for Differential Equations), a novel reinforcement learning-based approach that derives symbolic closed-form solutions for various differential equations. Evaluations across a diverse set of ordinary and partial differential equations demonstrate that SSDE outperforms existing machine learning methods, delivering superior accuracy and efficiency in obtaining analytical solutions.

Applications · Chemistry, Physics, and Earth Sciences

Long-Kai Huang, Rongyi Zhu, Bing He, Jianhua Yao

Protein Language Models (PLMs), pre-trained on extensive evolutionary data from natural proteins, have emerged as indispensable tools for protein design. While powerful, PLMs often struggle to produce proteins with precisely specified functionalities or properties due to inherent challenges in controlling their outputs. In this work, we investigate the potential of Activation Steering, a technique originally developed for controlling text generation in Large Language Models (LLMs), to direct PLMs toward generating protein sequences with targeted properties. We propose a simple yet effective method that employs activation editing to steer PLM outputs, and extend this approach to protein optimization through a novel editing site identification module. Through comprehensive experiments on lysozyme-like sequence generation and optimization, we demonstrate that our methods can be seamlessly integrated into both auto-encoding and autoregressive PLMs without requiring additional training. These results highlight a promising direction for precise protein engineering using foundation models.

Applications · Chemistry, Physics, and Earth Sciences

Karn Tiwari, Niladri Dutta, N M Anoop Krishnan, Prathosh AP

Neural operators have emerged as powerful data-driven frameworks for solving Partial Differential Equations (PDEs), offering significant speedups over numerical methods. However, existing neural operators struggle with scalability in high-dimensional spaces, incur high computational costs, and face challenges in capturing continuous and long-range dependencies in PDE dynamics. To address these limitations, we introduce the Latent Mamba Operator (LaMO), which integrates the efficiency of state-space models (SSMs) in latent space with the expressive power of kernel integral formulations in neural operators. We also establish a theoretical connection between state-space models (SSMs) and the kernel integral of neural operators. Extensive experiments across diverse PDE benchmarks on regular grids, structured meshes, and point clouds covering solid and fluid physics datasets, LaMOs achieve consistent state-of-the-art (SOTA) performance, with a 32.3\% improvement over existing baselines in solution operator approximation, highlighting its efficacy in modeling complex PDEs solution.