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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.

Reinforcement Learning · Deep RL

Yucen Wang, Rui Yu, Shenghua Wan, Le Gan, De-Chuan Zhan

Foundation Models (FMs) and World Models (WMs) offer complementary strengths in task generalization at different levels. In this work, we propose FOUNDER, a framework that integrates the generalizable knowledge embedded in FMs with the dynamic modeling capabilities of WMs to enable open-ended task solving in embodied environments in a reward-free manner. We learn a mapping function that grounds FM representations in the WM state space, effectively inferring the agent's physical states in the world simulator from external observations. This mapping enables the learning of a goal-conditioned policy through imagination during behavior learning, with the mapped task serving as the goal state. Our method leverages the predicted temporal distance to the goal state as an informative reward signal. FOUNDER demonstrates superior performance on various multi-task offline visual control benchmarks, excelling in capturing the deep-level semantics of tasks specified by text or videos, particularly in scenarios involving complex observations or domain gaps where prior methods struggle. The consistency of our learned reward function with the ground-truth reward is also empirically validated. Our project website is https://sites.google.com/view/founder-rl.

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 · Everything Else

Arturs Berzins, Andreas Radler, Eric Volkmann, Sebastian Sanokowski, Sepp Hochreiter, Johannes Brandstetter

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

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.

Position · Methodology

Yoonsoo Nam, Seok Hyeong Lee, Clémentine Dominé, Yeachan Park, Charles London, Wonyl Choi, Niclas Göring, Seungjai Lee

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural network dynamics. These models follow the dynamical feedback principle, which describes how layers mutually govern and amplify each other's evolution. This principle extends beyond the simplified models, successfully explaining a wide range of dynamical phenomena in deep neural networks, including neural collapse, emergence, lazy and rich regimes, and grokking. In this position paper, we call for the use of layerwise linear models retaining the core principles of neural dynamical phenomena to accelerate the science of deep learning.

Applications · Everything Else

Jesse He, Helen Jenne, Herman Chau, Davis Brown, Mark Raugas, Sara Billey, Henry Kvinge

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze. In this work, we use graph neural networks to investigate quiver mutation---an operation that transforms one quiver (or directed multigraph) into another---which is central to the theory of cluster algebras with deep connections to geometry, topology, and physics. In the study of cluster algebras, the question of mutation equivalence is of fundamental concern: given two quivers, can one efficiently determine if one quiver can be transformed into the other through a sequence of mutations? In this paper, we use graph neural networks and AI explainability techniques to independently discover mutation equivalence criteria for quivers of type $\tilde{D}$. Along the way, we also show that even without explicit training to do so, our model captures structure within its hidden representation that allows us to reconstruct known criteria from type $D$, adding to the growing evidence that modern machine learning models are capable of learning abstract and general rules from mathematical data.

Deep Learning · Algorithms

Jan Blechschmidt, Tom-Christian Riemer, Max Winkler, Martin STOLL, Jan-Frederik Pietschmann

We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport in biological cells to the motion of human crowds. While traditional numerical schemes require a large amount of tailoring, especially in the case of model design or parameter identification problems, physics informed deep operator networks (DeepONets) have emerged as a versatile tool for the solution of partial differential equations with the particular advantage that they easily incorporate parameter identification questions. We here present an approach where we first learn three DeepONet models for representative inflow, inner and outflow edges, resp., and then subsequently couple these models for the solution of the drift-diffusion metric graph problem by relying on an edge-based domain decomposition approach. We illustrate that our framework is applicable for the accurate evaluation of graph-coupled physics models and is well suited for solving optimization or inverse problems on these coupled networks.

Applications · Chemistry, Physics, and Earth Sciences

Runzhong Wang, Rui-Xi Wang, Mrunali Manjrekar, Connor Coley

Molecular machine learning has gained popularity with the advancements of geometric deep learning. In parallel, retrieval-augmented generation has become a principled approach commonly used with language models. However, the optimal integration of retrieval augmentation into molecular machine learning remains unclear. Graph neural networks stand to benefit from clever matching to understand the structural alignment of retrieved molecules to a query molecule. Neural graph matching offers a compelling solution by explicitly modeling node and edge affinities between two structural graphs while employing a noise-robust, end-to-end neural network to learn affinity metrics. We apply this approach to mass spectrum simulation and introduce MARASON, a novel model that incorporates neural graph matching to enhance a fragmentation-based neural network. Experimental results highlight the effectiveness of our design, with MARASON achieving 27% top-1 accuracy, a substantial improvement over the non-retrieval state-of-the-art accuracy of 19%. Moreover, MARASON outperforms both naive retrieval-augmented generation methods and traditional graph matching approaches. Code is publicly available at https://github.com/coleygroup/ms-pred.

Deep Learning · Attention Mechanisms

Greyson Brothers

We investigate the design of pooling methods used to summarize the outputs of transformer embedding models, primarily motivated by reinforcement learning and vision applications. This work considers problems where a subset of the input vectors contains requisite information for a downstream task (signal) while the rest are distractors (noise). By framing pooling as vector quantization with the goal of minimizing signal loss, we demonstrate that the standard methods used to aggregate transformer outputs, AvgPool, MaxPool, and ClsToken, are vulnerable to performance collapse as the signal-to-noise ratio (SNR) of inputs fluctuates. We then show that an attention-based *adaptive pooling* method can approximate the signal-optimal vector quantizer within derived error bounds for any SNR. Our theoretical results are first validated by supervised experiments on a synthetic dataset designed to isolate the SNR problem, then generalized to standard relational reasoning, multi-agent reinforcement learning, and vision benchmarks with noisy observations, where transformers with adaptive pooling display superior robustness across tasks.

Applications · Robotics

Lucy Xiaoyang Shi, brian ichter, Michael Equi, Liyiming Ke, Karl Pertsch, Quan Vuong, James Tanner, Anna Walling, Haohuan Wang, Niccolo Fusai 等

Generalist robots that can perform a range of different tasks in open-world settings must be able to not only reason about the steps needed to accomplish their goals, but also process complex instructions, prompts, and even feedback during task execution. Intricate instructions (e.g., "Could you make me a vegetarian sandwich?" or "I don't like that one") require not just the ability to physically perform the individual steps, but the ability to situate complex commands and feedback in the physical world. In this work, we describe a system that uses vision-language models in a hierarchical structure, first reasoning over complex prompts and user feedback to deduce the most appropriate next step to fulfill the task, and then performing that step with low-level actions. In contrast to direct instruction following methods that can fulfill simple commands ("pick up the cup"), our system can reason through complex prompts and incorporate situated feedback during task execution ("that's not trash"). We evaluate our system across three robotic platforms, including single-arm, dual-arm, and dual-arm mobile robots, demonstrating its ability to handle tasks such as cleaning messy tables, making sandwiches, and grocery shopping.Videos are available at https://www.pi.website/research/hirobot

Applications · Chemistry, Physics, and Earth Sciences

Jaeheun Jung, Jaehyuk Lee, ChangHae Jung, Hanyoung Kim, Bosung Jung, Donghun Lee

Shock waves caused by earthquakes can be devastating. Generating realistic earthquake-caused ground motion waveforms help reducing losses in lives and properties, yet generative models for the task tend to generate subpar waveforms. We present High-fidelity Earthquake Groundmotion Generation System (HEGGS) and demonstrate its superior performance using earthquakes from North American, East Asian, and European regions. HEGGS exploits the intrinsic characteristics of earthquake dataset and learns the waveforms using an end-to-end differentiable generator containing conditional latent diffusion model and hi-fidelity waveform construction model. We show the learning efficiency of HEGGS by training it on a single GPU machine and validate its performance using earthquake databases from North America, East Asia, and Europe, using diverse criteria from waveform generation tasks and seismology. Once trained, HEGGS can generate three dimensional E-N-Z seismic waveforms with accurate P/S phase arrivals, envelope correlation, signal-to-noise ratio, GMPE analysis, frequency content analysis, and section plot analysis.

Applications · Chemistry, Physics, and Earth Sciences

Nikita Kazeev, Wei Nong, Ignat Romanov, Ruiming Zhu, Andrey Ustyuzhanin, Shuya Yamazaki, Kedar Hippalgaonkar

Crystal symmetry plays a fundamental role in determining its physical, chemical, and electronic properties such as electrical and thermal conductivity, optical and polarization behavior, and mechanical strength. Almost all known crystalline materials have internal symmetry. However, this is often inadequately addressed by existing generative models, making the consistent generation of stable and symmetrically valid crystal structures a significant challenge. We introduce WyFormer, a generative model that directly tackles this by formally conditioning on space group symmetry. It achieves this by using Wyckoff positions as the basis for an elegant, compressed, and discrete structure representation. To model the distribution, we develop a permutation-invariant autoregressive model based on the Transformer encoder and an absence of positional encoding. Extensive experimentation demonstrates WyFormer's compelling combination of attributes: it achieves best-in-class symmetry-conditioned generation, incorporates a physics-motivated inductive bias, produces structures with competitive stability, predicts material properties with competitive accuracy even without atomic coordinates, and exhibits unparalleled inference speed.

Applications · Chemistry, Physics, and Earth Sciences

Rudy Morel, Jiequn Han, Edouard Oyallon

We address the problem of predicting the next states of a dynamical system governed by *unknown* temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to this task, the presence of a well-structured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next states through time integration. Our framework decouples dynamics estimation -- i.e., DISCovering an evolution Operator from a short trajectory -- from state prediction -- i.e., evolving this operator. Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well to unseen initial conditions and remains competitive when fine-tuned on downstream tasks.

Deep Learning · Generative Models and Autoencoders

Alexander Lobashev, Dmitry Guskov, Maria Larchenko, Mikhail Tamm

This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the posterior distribution of latent variables given generated samples and uses this to learn the log-partition function, which defines the Fisher metric for exponential families. Theoretical convergence guarantees are provided, and the method is validated on the Ising and TASEP models, outperforming existing baselines in reconstructing thermodynamic quantities. Applied to diffusion models, the method reveals a fractal structure of phase transitions in the latent space, characterized by abrupt changes in the Fisher metric. We demonstrate that while geodesic interpolations are approximately linear within individual phases, this linearity breaks down at phase boundaries, where the diffusion model exhibits a divergent Lipschitz constant with respect to the latent space. These findings provide new insights into the complex structure of diffusion model latent spaces and their connection to phenomena like phase transitions.Our source code is available at \url{https://github.com/alobashev/hessian-geometry-of-diffusion-models}.

Deep Learning · Algorithms

Hang Zhou, Yuezhou Ma, Haixu Wu, Haowen Wang, Mingsheng Long

Deep models have recently emerged as promising tools to solve partial differential equations (PDEs), known as neural PDE solvers. While neural solvers trained from either simulation data or physics-informed loss can solve PDEs reasonably well, they are mainly restricted to a few instances of PDEs, e.g. a certain equation with a limited set of coefficients. This limits their generalization to diverse PDEs, preventing them from being practical surrogate models of numerical solvers. In this paper, we present Unisolver, a novel Transformer model trained on diverse data and conditioned on diverse PDEs, aiming towards a universal neural PDE solver capable of solving a wide scope of PDEs. Instead of purely scaling up data and parameters, Unisolver stems from the theoretical analysis of the PDE-solving process. Inspired by the mathematical structure of PDEs that a PDE solution is fundamentally governed by a series of PDE components such as equation symbols and boundary conditions, we define a complete set of PDE components and flexibly embed them as domain-wise and point-wise deep conditions for Transformer PDE solvers. Integrating physical insights with recent Transformer advances, Unisolver achieves consistent state-of-the-art on three challenging large-scale benchmarks, showing impressive performance and generalizability. Code is available at [https://github.com/thuml/Unisolver](https://github.com/thuml/Unisolver).

Applications · Chemistry, Physics, and Earth Sciences

David K Park, Xihaier Luo, Guang Zhao, Seungjun Lee, Miruna Oprescu, Shinjae Yoo

Spatiotemporal learning is challenging due to the intricate interplay between spatial and temporal dependencies, the high dimensionality of the data, and scalability constraints. These challenges are further amplified in scientific domains, where data is often irregularly distributed (e.g., missing values from sensor failures) and high-volume (e.g., high-fidelity simulations), posing additional computational and modeling difficulties. In this paper, we present SCENT, a novel framework for scalable and continuity-informed spatiotemporal representation learning. SCENT unifies interpolation, reconstruction, and forecasting within a single architecture. Built on a transformer-based encoder-processor-decoder backbone, SCENT introduces learnable queries to enhance generalization and a query-wise cross-attention mechanism to effectively capture multi-scale dependencies. To ensure scalability in both data size and model complexity, we incorporate a sparse attention mechanism, enabling flexible output representations and efficient evaluation at arbitrary resolutions. We validate SCENT through extensive simulations and real-world experiments, demonstrating state-of-the-art performance across multiple challenging tasks while achieving superior scalability.