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Applications · Chemistry, Physics, and Earth Sciences

Benedikt Böck, Andreas Oeldemann, Timo Mayer, Francesco Rossetto, Wolfgang Utschick

Learning the site-specific distribution of the wireless channel within a particular environment of interest is essential to exploit the full potential of machine learning (ML) for wireless communications and radar applications. Generative modeling offers a promising framework to address this problem. However, existing approaches pose unresolved challenges, including the need for high-quality training data, limited generalizability, and a lack of physical interpretability. To address these issues, we combine the physics-related compressibility of wireless channels with generative modeling, in particular, sparse Bayesian generative modeling (SBGM), to learn the distribution of the underlying physical channel parameters. By leveraging the sparsity-inducing characteristics of SBGM, our methods can learn from compressed observations received by an access point (AP) during default online operation. Moreover, they are physically interpretable and generalize over system configurations without requiring retraining.

Applications · Chemistry, Physics, and Earth Sciences

Wenzhi Feng, Xutao Li, Zhe Wu, Kenghong Lin, Demin Yu, Yunming Ye, Yaowei Wang

Most current precipitation nowcasting methods aim to capture the underlying spatiotemporal dynamics of precipitation systems by minimizing the mean square error (MSE). However, these methods often neglect effective constraints on the data distribution, leading to unsatisfactory prediction accuracy and image quality, especially for long forecast sequences. To address this limitation, we propose a precipitation nowcasting model incorporating perceptual constraints. This model reformulates precipitation nowcasting as a posterior MSE problem under such constraints. Specifically, we first obtain the posteriori mean sequences of precipitation forecasts using a precipitation estimator. Subsequently, we construct the transmission between distributions using rectified flow. To enhance the focus on distant frames, we design a frame sampling strategy that gradually increases the corresponding weights. We theoretically demonstrate the reliability of our solution, and experimental results on two publicly available radar datasets demonstrate that our model is effective and outperforms current state-of-the-art models.

Applications · Chemistry, Physics, and Earth Sciences

Vsevolod Viliuga, Leif Seute, Nicolas Wolf, Simon Wagner, Arne Elofsson, Jan Stuehmer, Frauke Gräter

Recent advances in geometric deep learning and generative modeling have enabled the design of novel proteins with a wide range of desired properties. However, current state-of-the-art approaches are typically restricted to generating proteins with only static target properties, such as motifs and symmetries. In this work, we take a step towards overcoming this limitation by proposing a framework to condition structure generation on flexibility, which is crucial for key functionalities such as catalysis or molecular recognition. We first introduce BackFlip, an equivariant neural network for predicting per-residue flexibility from an input backbone structure. Relying on BackFlip, we propose FliPS, an SE(3)-equivariant conditional flow matching model that solves the inverse problem, that is, generating backbones that display a target flexibility profile. In our experiments, we show that FliPS is able to generate novel and diverse protein backbones with the desired flexibility, verified by Molecular Dynamics (MD) simulations.

Applications · Chemistry, Physics, and Earth Sciences

Yunfei Huang, David S. Greenberg

Neural PDE surrogates can improve the cost-accuracy tradeoff of classical solvers, but often generalize poorly to new initial conditions and accumulate errors over time. Physical and symmetry constraints have shown promise in closing this performance gap, but existing techniques for imposing these inductive biases are incompatible with the staggered grids commonly used in computational fluid dynamics. Here we introduce novel input and output layers that respect physical laws and symmetries on the staggered grids, and for the first time systematically investigate how these constraints, individually and in combination, affect the accuracy of PDE surrogates. We focus on two challenging problems: shallow water equations with closed boundaries and decaying incompressible turbulence. Compared to strong baselines, symmetries and physical constraints consistently improve performance across tasks, architectures, autoregressive prediction steps, accuracy measures, and network sizes. Symmetries are more effective than physical constraints, but surrogates with both performed best, even compared to baselines with data augmentation or pushforward training, while themselves benefiting from the pushforward trick. Doubly-constrained surrogates also generalize better to initial conditions and durations beyond the range of the training data, and more accurately predict real-world ocean currents.

Applications · Chemistry, Physics, and Earth Sciences

Urszula Julia Komorowska, Francisco Vargas, Alessandro Rondina, Pietro Lió, Mateja Jamnik

Protein's backbone flexibility is a crucial property that heavily influences its functionality. Recent work in the field of protein diffusion probabilistic modelling has leveraged Normal Mode Analysis (NMA) and, for the first time, introduced information about large scale protein motion into the generative process. However, obtaining molecules with both the desired dynamics and designable quality has proven challenging. In this work, we present NMA-tune, a new method that introduces the dynamics information to the protein design stage. NMA-tune uses a trainable component to condition the backbone generation on the lowest normal mode of oscillation. We implement NMA-tune as a plug-and-play extension to RFdiffusion, show that the proportion of samples with high quality structure and the desired dynamics is improved as compared to other methods without the trainable component, and we show the presence of the targeted modes in the Molecular Dynamics simulations.

Applications · Chemistry, Physics, and Earth Sciences

Fanmeng Wang, Minjie Cheng, Hongteng Xu

Predicting molecular ground-state conformation (i.e., energy-minimized conformation) is crucial for many chemical applications such as molecular docking and property prediction. Classic energy-based simulation is time-consuming when solving this problem, while existing learning-based methods have advantages in computational efficiency but sacrifice accuracy and interpretability.In this work, we propose a novel and effective method to bridge the energy-based simulation and the learning-based strategy, which designs and learns a Wasserstein gradient flow-driven SE(3)-Transformer, called WGFormer, for ground-state conformation prediction. Specifically, our method tackles this task within an auto-encoding framework, which encodes low-quality conformations by the proposed WGFormer and decodes corresponding ground-state conformations by an MLP.The architecture of WGFormer corresponds to Wasserstein gradient flows --- it optimizes conformations by minimizing an energy function defined on the latent mixture models of atoms, thereby significantly improving performance and interpretability.Extensive experiments demonstrate that our method consistently outperforms state-of-the-art competitors, providing a new and insightful paradigm to predict ground-state conformation.The code is available at https://github.com/FanmengWang/WGFormer.

Applications · Chemistry, Physics, and Earth Sciences

Benjamin Holzschuh, Qiang Liu, Georg Kohl, Nils Thuerey

We introduce PDE-Transformer, an improved transformer-based architecture for surrogate modeling of physics simulations on regular grids. We combine recent architectural improvements of diffusion transformers with adjustments specific for large-scale simulations to yield a more scalable and versatile general-purpose transformer architecture, which can be used as the backbone for building large-scale foundation models in physical sciences. We demonstrate that our proposed architecture outperforms state-of-the-art transformer architectures for computer vision on a large dataset of 16 different types of PDEs. We propose to embed different physical channels individually as spatio-temporal tokens, which interact via channel-wise self-attention. This helps to maintain a consistent information density of tokens when learning multiple types of PDEs simultaneously. We demonstrate that our pre-trained models achieve improved performance on several challenging downstream tasks compared to training from scratch and also beat other foundation model architectures for physics simulations.Our source code is available at https://github.com/tum-pbs/pde-transformer.

Applications · Chemistry, Physics, and Earth Sciences

Chuqi CHEN, Yahong Yang, Yang Xiang, Wenrui Hao

Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters in the PDEs that introduce near-singularities in the loss function. In this study, we overcome this challenge by introducing a novel method based on homotopy dynamics to effectively manipulate these parameters. From a theoretical perspective, we analyze the effects of these parameters on training difficulty in these singularly perturbed problems and establish the convergence of the proposed homotopy dynamics method. Experimentally, we demonstrate that our approach significantly accelerates convergence and improves the accuracy of these singularly perturbed problems. These findings present an efficient optimization strategy leveraging homotopy dynamics, offering a robust framework to extend the applicability of neural networks for solving singularly perturbed differential equations.

Applications · Chemistry, Physics, and Earth Sciences

Chris Pedersen, Laure Zanna, Joan Bruna

Autoregressive surrogate models (or *emulators*) of spatiotemporal systems provide an avenue for fast, approximate predictions, with broad applications across science and engineering. At inference time however, these models are generally unable to provide predictions over long time rollouts due to accumulation of errors leading to diverging trajectories. In essence, emulators operate out of distribution, and controlling the online distribution quickly becomes intractable in large-scale settings. To address this fundamental issue, and focusing on time-stationary systems admitting an invariant measure, we leverage diffusion models to obtain an implicit estimator of the score of this invariant measure. We show that this model of the score function can be used to stabilize autoregressive emulator rollouts by applying on-the-fly denoising during inference, a process we call *thermalization*. Thermalizing an emulator rollout is shown to extend the time horizon of stable predictions by two orders of magnitude in complex systems exhibiting turbulent and chaotic behavior, opening up a novel application of diffusion models in the context of neural emulation.

Applications · Chemistry, Physics, and Earth Sciences

Haoyang Jiang, Jindong Wang, Xingquan Zhu, Yi He

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal. To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.

Applications · Chemistry, Physics, and Earth Sciences

Ruizhe Chen, Dongyu Xue, Xiangxin Zhou, Zaixiang Zheng, xiangxiang Zeng, Quanquan Gu

Proteins typically exist in complexes, interacting with other proteins or biomolecules to perform their specific biological roles. Research on single-chain protein modeling has been extensively and deeply explored, with advancements seen in models like the series of ESM and AlphaFold2. Despite these developments, the study and modeling of multi-chain proteins remain largely uncharted, though they are vital for understanding biological functions. Recognizing the importance of these interactions, we introduce APM (all-Atom Protein generative Model), a model specifically designed for modeling multi-chain proteins. By integrating atom-level information and leveraging data on multi-chain proteins, APM is capable of precisely modeling inter-chain interactions and designing protein complexes with binding capabilities from scratch. It also performs folding and inverse-folding tasks for multi-chain proteins. Moreover, APM demonstrates versatility in downstream applications: it achieves enhanced performance through supervised fine-tuning (SFT) while also supporting zero-shot sampling in certain tasks, achieving state-of-the-art results. We released our code at https://github.com/bytedance/apm.

Applications · Chemistry, Physics, and Earth Sciences

Keyue Qiu, Yuxuan Song, Jie Yu, Hongbo Ma, Ziyao Cao, Zhilong Zhang, Yushuai Wu, Mingyue Zheng, Hao Zhou, Wei-Ying Ma

Structure-based molecule optimization (SBMO) aims to optimize molecules with both continuous coordinates and discrete types against protein targets.A promising direction is to exert gradient guidance on generative models given its remarkable success in images, but it is challenging to guide discrete data and risks inconsistencies between modalities.To this end, we leverage a continuous and differentiable space derived through Bayesian inference, presenting Molecule Joint Optimization (MolJO), the gradient-based SBMO framework that facilitates joint guidance signals across different modalities while preserving SE(3)-equivariance.We introduce a novel backward correction strategy that optimizes within a sliding window of the past histories, allowing for a seamless trade-off between explore-and-exploit during optimization.MolJO achieves state-of-the-art performance on CrossDocked2020 benchmark (Success Rate 51.3\%, Vina Dock -9.05 and SA 0.78), more than 4x improvement in Success Rate compared to the gradient-based counterpart, and 2x ``Me-Better'' Ratio as much as 3D baselines. Furthermore, we extend MolJO to a wide range of optimization settings, including multi-objective optimization and challenging tasks in drug design such as R-group optimization and scaffold hopping, further underscoring its versatility.Code is available at https://github.com/AlgoMole/MolCRAFT.

Applications · Chemistry, Physics, and Earth Sciences

Sai Advaith Maddipatla, Nadav Bojan, Meital Bojan, Sanketh Vedula, Paul Schanda, Ailie Marx, Alexander Bronstein

Proteins exist as a dynamic ensemble of multiple conformations, and these motions are often crucial for their functions. However, current structure prediction methods predominantly yield a single conformation, overlooking the conformational heterogeneity revealed by diverse experimental modalities. Here, we present a framework for building experiment-grounded protein structure generative models that infer conformational ensembles consistent with measured experimental data. The key idea is to treat state-of-the-art protein structure predictors (e.g., AlphaFold3) as sequence-conditioned structural priors, and cast ensemble modeling as posterior inference of protein structures given experimental measurements. Through extensive real-data experiments, we demonstrate the generality of our method to incorporate a variety of experimental measurements. In particular, our framework uncovers previously unmodeled conformational heterogeneity from crystallographic densities, generates high-accuracy NMR ensembles orders of magnitude faster than status quo, and incorporates pairwise cross-link constraints. Notably, we demonstrate that our ensembles outperform AlphaFold3 and sometimes better fit experimental data than publicly deposited structures to the protein database (PDB). We believe that this approach will unlock building predictive models that fully embrace experimentally observed conformational diversity.

Applications · Chemistry, Physics, and Earth Sciences

Seul Lee, Karsten Kreis, Srimukh Veccham, Meng Liu, Danny Reidenbach, Yuxing Peng, Saee Paliwal, Weili Nie, Arash Vahdat

Drug discovery is a complex process that involves multiple stages and tasks. However, existing molecular generative models can only tackle some of these tasks. We present *Generalist Molecular generative model* (GenMol), a versatile framework that uses only a *single* discrete diffusion model to handle diverse drug discovery scenarios. GenMol generates Sequential Attachment-based Fragment Embedding (SAFE) sequences through non-autoregressive bidirectional parallel decoding, thereby allowing the utilization of a molecular context that does not rely on the specific token ordering while having better sampling efficiency. GenMol uses fragments as basic building blocks for molecules and introduces *fragment remasking*, a strategy that optimizes molecules by regenerating masked fragments, enabling effective exploration of chemical space. We further propose *molecular context guidance* (MCG), a guidance method tailored for masked discrete diffusion of GenMol. GenMol significantly outperforms the previous GPT-based model in *de novo* generation and fragment-constrained generation, and achieves state-of-the-art performance in goal-directed hit generation and lead optimization. These results demonstrate that GenMol can tackle a wide range of drug discovery tasks, providing a unified and versatile approach for molecular design.

Applications · Chemistry, Physics, and Earth Sciences

Jian Gao, Weidong Cao, Xuan Zhang

The sustainable performance improvements of integrated circuits (ICs) drive the continuous advancement of nearly all transformative technologies. Since its invention, IC performance enhancements have been dominated by scaling the semiconductor technology. Yet, as Moore's law tapers off, a crucial question arises: ***How can we sustain IC performance in the post-Moore era?*** Creating new circuit topologies has emerged as a promising pathway to address this fundamental need. This work proposes AnalogGenie-Lite, a decoder-only transformer that discovers novel analog IC topologies with significantly enhanced scalability and precision via lightweight graph modeling.AnalogGenie-Lite makes several unique contributions, including concise device-pin representations (i.e., advancing the best prior art from $O\left(n^2\right)$ to $O\left(n\right)$), frequent sub-graph mining, and optimal sequence modeling. Compared to state-of-the-art circuit topology discovery methods, it achieves $5.15\times$ to $71.11\times$ gains in scalability and 23.5\% to 33.6\% improvements in validity. Case studies on other domains' graphs are also provided to show the broader applicability of the proposed graph modeling approach. Source code: https://github.com/xz-group/AnalogGenie-Lite.

Applications · Chemistry, Physics, and Earth Sciences

Charlie Tan, Joey Bose, Chen Lin, Leon Klein, Michael Bronstein, Alexander Tong

Scalable sampling of molecular states in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators tackle this problem by pairing normalizing flows with importance sampling to obtain uncorrelated samples under the target distribution. In this paper, we extend the Boltzmann generator framework with two key contributions, denoting our framework Sequential Boltzmann Generators (SBG). The first is a highly efficient Transformer-based normalizing flow operating directly on all-atom Cartesian coordinates. In contrast to the equivariant continuous flows of prior methods, we leverage exactly invertible non-equivariant architectures which are highly efficient during both sample generation and likelihood evaluation. This efficiency unlocks more sophisticated inference strategies beyond standard importance sampling. In particular, we perform inference-time scaling of flow samples using a continuous-time variant of sequential Monte Carlo, in which flow samples are transported towards the target distribution with annealed Langevin dynamics. SBG achieves state-of-the-art performance w.r.t. all metrics on peptide systems, demonstrating the first equilibrium sampling in Cartesian coordinates of tri-, tetra- and hexa-peptides that were thus far intractable for prior Boltzmann generators.

Applications · Chemistry, Physics, and Earth Sciences

Jiahe Du, Kaixiong Zhou, Xinyu Hong, Zhaozhuo Xu, Jinbo Xu, Xiao Huang

Generating novel enzymes for target molecules in zero-shot scenarios is a fundamental challenge in biomaterial synthesis and chemical production. Without known enzymes for a target molecule, training generative models becomes difficult due to the lack of direct supervision. To address this, we propose a retrieval-augmented generation method that uses existing enzyme-substrate data to guide enzyme design. Our method retrieves enzymes with substrates that share structural similarities with the target molecule, leveraging functional similarities in catalytic activity. Since none of the retrieved enzymes directly catalyze the target molecule, we use a conditioned discrete diffusion model to generate new enzymes based on the retrieved examples. An enzyme-substrate relationship classifier guides the generation process to ensure optimal protein sequence distributions. We evaluate our model on enzyme design tasks with diverse real-world substrates and show that it outperforms existing protein generation methods in catalytic capability, foldability, and docking accuracy. Additionally, we define the zero-shot substrate-specified enzyme generation task and introduce a dataset with evaluation benchmarks.

Applications · Chemistry, Physics, and Earth Sciences

Filippo Bigi, Marcel Langer, Michele Ceriotti

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have revolutionized the fields of computational chemistry and materials discovery.In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically constrained approach, suggesting that directly predicting the forces yields a better trade-off between accuracy and computational efficiency -- and that energy conservation can be learned during training.This work investigates the applicability of such non-conservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics.Contrary to the case of rotational symmetry, energy conservation is hard to learn, monitor, and correct for.The best approach to exploit the acceleration afforded by direct force prediction might be to use it in tandem with a conservative model, reducing -- rather than eliminating -- the additional cost of backpropagation, but avoiding the pathological behavior associated with non-conservative forces.

Applications · Chemistry, Physics, and Earth Sciences

Filip Ekström Kelvinius, Oskar Andersson, Abhijith Parackal, Dong Qian, Rickard Armiento, Fredrik Lindsten

Crystalline materials often exhibit a high level of symmetry. However, most generative models do not account for symmetry, but rather model each atom without any constraints on its position or element. We propose a generative model, Wyckoff Diffusion (WyckoffDiff), which generates symmetry-based descriptions of crystals. This is enabled by considering a crystal structure representation that encodes all symmetry, and we design a novel neural network architecture which enables using this representation inside a discrete generative model framework. In addition to respecting symmetry by construction, the discrete nature of our model enables fast generation. We additionally present a new metric, Fréchet Wrenformer Distance, which captures the symmetry aspects of the materials generated, and we benchmark WyckoffDiff against recently proposed generative models for crystal generation. As a proof-of-concept study, we use WyckoffDiff to find new materials below the convex hull of thermodynamical stability.

Applications · Chemistry, Physics, and Earth Sciences

Pengkang Guo, Bruno Correia, Pierre Vandergheynst, Daniel Probst

Machine learning for protein modeling faces significant challenges due to proteins' inherently dynamic nature, yet most graph-based machine learning methods rely solely on static structural information. Recently, the growing availability of molecular dynamics trajectories provides new opportunities for understanding the dynamic behavior of proteins; however, computational methods for utilizing this dynamic information remain limited. We propose a novel graph representation that integrates both static structural information and dynamic correlations from molecular dynamics trajectories, enabling more comprehensive modeling of proteins. By applying relational graph neural networks (RGNNs) to process this heterogeneous representation, we demonstrate significant improvements over structure-based approaches across three distinct tasks: atomic adaptability prediction, binding site detection, and binding affinity prediction. Our results validate that combining static and dynamic information provides complementary signals for understanding protein-ligand interactions, offering new possibilities for drug design and structural biology applications.