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Applications · Language, Speech and Dialog

Yuhang He, Anoop Cherian, Gordon Wichern, Andrew Markham

The primary objective of room acoustics is to model the intricate sound propagation dynamics from any source to receiver position within enclosed 3D spaces. These dynamics are encapsulated in the form of a 1D room impulse response (RIR). Precisely measuring RIR is difficult due to the complexity of sound propagation encompassing reflection, diffraction, and absorption. In this work, we propose to learn a continuous neural room acoustics field that implicitly encodes all essential sound propagation primitives for each enclosed 3D space, so that we can infer the RIR corresponding to arbitrary source-receiver positions unseen in the training dataset. Our framework, dubbed DeepNeRAP, is trained in a self-supervised manner without requiring direct access to RIR ground truth that is often needed in prior methods. The key idea is to design two cooperative acoustic agents to actively probe a 3D space, one emitting and the other receiving sound at various locations. Analyzing this sound helps to inversely characterize the acoustic primitives. Our framework is well-grounded in the fundamental physical principles of sound propagation, including reciprocity and globality, and thus is acoustically interpretable and meaningful. We present experiments on both synthetic and real-world datasets, demonstrating superior quality in RIR estimation against closely related methods.

Applications · Physics

Jan Hagnberger, Marimuthu Kalimuthu, Daniel Musekamp, Mathias Niepert

Transformer models are increasingly used for solving Partial Differential Equations (PDEs). Several adaptations have been proposed, all of which suffer from the typical problems of Transformers, such as quadratic memory and time complexity. Furthermore, all prevalent architectures for PDE solving lack at least one of several desirable properties of an ideal surrogate model, such as (i) generalization to PDE parameters not seen during training, (ii) spatial and temporal zero-shot super-resolution, (iii) continuous temporal extrapolation, (iv) support for 1D, 2D, and 3D PDEs, and (v) efficient inference for longer temporal rollouts. To address these limitations, we propose *Vectorized Conditional Neural Fields* (VCNeFs), which represent the solution of time-dependent PDEs as neural fields. Contrary to prior methods, however, VCNeFs compute, for a set of multiple spatio-temporal query points, their solutions in parallel and model their dependencies through attention mechanisms. Moreover, VCNeF can condition the neural field on both the initial conditions and the parameters of the PDEs. An extensive set of experiments demonstrates that VCNeFs are competitive with and often outperform existing ML-based surrogate models.

Deep Learning · Generative Models and Autoencoders

Nate Gillman, Michael Freeman, Daksh Aggarwal, Chia-Hong HSU, Calvin Luo, Yonglong Tian, Chen Sun

As synthetic data becomes higher quality and proliferates on the internet, machine learning models are increasingly trained on a mix of human- and machine-generated data. Despite the successful stories of using synthetic data for representation learning, using synthetic data for generative model training creates ``self-consuming loops'' which may lead to training instability or even collapse, unless certain conditions are met. Our paper aims to stabilize self-consuming generative model training. Our theoretical results demonstrate that by introducing an idealized correction function, which maps a data point to be more likely under the true data distribution, self-consuming loops can be made *exponentially* more stable. We then propose self-correction functions, which rely on expert knowledge (e.g. the laws of physics programmed in a simulator), and aim to approximate the idealized corrector automatically and at scale. We empirically validate the effectiveness of self-correcting self-consuming loops on the challenging human motion synthesis task, and observe that it successfully avoids model collapse, even when the ratio of synthetic data to real data is as high as 100%.

Applications · Physics

Junfeng CHEN, Kailiang Wu

Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems. Transformers with the self-attention mechanism---a powerful tool originally designed for natural language processing---have recently been adapted for operator learning. However, they confront challenges, including high computational demands and limited interpretability. This raises a critical question: *Is there a more efficient attention mechanism for Transformer-based operator learning?* This paper proposes the Position-induced Transformer (PiT), built on an innovative position-attention mechanism, which demonstrates significant advantages over the classical self-attention in operator learning. Position-attention draws inspiration from numerical methods for PDEs. Different from self-attention, position-attention is induced by only the spatial interrelations of sampling positions for input functions of the operators, and does not rely on the input function values themselves, thereby greatly boosting efficiency. PiT exhibits superior performance over current state-of-the-art neural operators in a variety of complex operator learning tasks across diverse PDE benchmarks. Additionally, PiT possesses an enhanced discretization convergence feature, compared to the widely-used Fourier neural operator.

Yifan Chen, Mark Goldstein, Mengjian Hua, Michael Albergo, Nicholas Boffi, Eric Vanden-Eijnden

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of the future system state given its current state. To this end, we leverage the framework of stochastic interpolants, which facilitates the construction of a generative model between an arbitrary base distribution and the target. We design a fictitious, non-physical stochastic dynamics that takes as initial condition the current system state and produces as output a sample from the target conditional distribution in finite time and without bias. This process therefore maps a point mass centered at the current state onto a probabilistic ensemble of forecasts. We prove that the drift coefficient entering the stochastic differential equation (SDE) achieving this task is non-singular, and that it can be learned efficiently by square loss regression over the time-series data. We show that the drift and the diffusion coefficients of this SDE can be adjusted after training, and that a specific choice that minimizes the impact of the estimation error gives a Föllmer process. We highlight the utility of our approach on several complex, high-dimensional forecasting problems, including stochastically forced Navier-Stokes and video prediction on the KTH and CLEVRER datasets. The code is available at https://github.com/interpolants/forecasting.

Applications · Physics

Jules Berman, Benjamin Peherstorfer

This work introduces reduced models based on Continuous Low Rank Adaptation (CoLoRA) that pre-train neural networks for a given partial differential equation and then continuously adapt low-rank weights in time to rapidly predict the evolution of solution fields at new physics parameters and new initial conditions. The adaptation can be either purely data-driven or via an equation-driven variational approach that provides Galerkin-optimal approximations. Because CoLoRA approximates solution fields locally in time, the rank of the weights can be kept small, which means that only few training trajectories are required offline so that CoLoRA is well suited for data-scarce regimes. Predictions with CoLoRA are orders of magnitude faster than with classical methods and their accuracy and parameter efficiency is higher compared to other neural network approaches.

Deep Learning · Large Language Models

Zeyuan Allen-Zhu, Yuanzhi Li

Large language models (LLMs) can store a vast amount of world knowledge, often extractable via question-answering (e.g., "What is Abraham Lincoln's birthday?''). However, do they answer such questions based on exposure to similar questions during training (i.e., cheating), or by genuinely learning to extract knowledge from sources like Wikipedia? In this paper, we investigate this issue using a controlled biography dataset. We find a strong correlation between the model's ability to extract knowledge and various _diversity measures_ of the training data. **Essentially**, for knowledge to be reliably extracted, it must be sufficiently augmented (e.g., through paraphrasing, sentence shuffling) _during pretraining_. Without such augmentation, knowledge may be memorized but not extractable, leading to 0% accuracy, regardless of subsequent instruction fine-tuning. To understand why this occurs, we employ (nearly) linear probing to demonstrate a strong connection between the observed correlation and _how the model internally encodes knowledge_ --- whether it is linearly encoded in the hidden embeddings of entity names or distributed across other token embeddings in the training text. **This paper provides several key recommendations for LLM pretraining in the industry:** (1) rewrite the pretraining data --- using small, auxiliary models --- to provide knowledge augmentation, and (2) incorporate more instruction-finetuning data into the pretraining stage before it becomes too late.

Applications · Physics

Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, Noseong Park

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Raynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known “failure modes”.

Applications · Chemistry and Drug Discovery

Tianlang Chen, Shengjie Luo, Di He, Shuxin Zheng, Tie-Yan Liu, Liwei Wang

Molecular modeling, a central topic in quantum mechanics, aims to accurately calculate the properties and simulate the behaviors of molecular systems. The molecular model is governed by physical laws, which impose geometric constraints such as invariance and equivariance to coordinate rotation and translation. While numerous deep learning approaches have been developed to learn molecular representations under these constraints, most of them are built upon heuristic and costly modules. We argue that there is a strong need for a general and flexible framework for learning both invariant and equivariant features. In this work, we introduce a novel Transformer-based molecular model called GeoMFormer to achieve this goal. Using the standard Transformer modules, two separate streams are developed to maintain and learn invariant and equivariant representations. Carefully designed _cross-attention_ modules bridge the two streams, allowing information fusion and enhancing geometric modeling in each stream. As a general and flexible architecture, we show that many previous architectures can be viewed as special instantiations of GeoMFormer. Extensive experiments are conducted to demonstrate the power of GeoMFormer. All empirical results show that GeoMFormer achieves strong performance on both invariant and equivariant tasks of different types and scales. Code and models will be made publicly available at https://github.com/c-tl/GeoMFormer.

Applications · Physics

Phong Nguyen, Xinlun Cheng, Shahab Azarfar, Pradeep Seshadri, Yen Nguyen, Munho Kim, Sanghun Choi, H. Udaykumar, Stephen Baek

Modeling unsteady, fast transient, and advection-dominated physics problems is a pressing challenge for physics-aware deep learning (PADL). The physics of complex systems is governed by large systems of partial differential equations (PDEs) and ancillary constitutive models with nonlinear structures, as well as evolving state fields exhibiting sharp gradients and rapidly deforming material interfaces. Here, we investigate an inductive bias approach that is versatile and generalizable to model generic nonlinear field evolution problems. Our study focuses on the recent physics-aware recurrent convolutions (PARC), which incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We extend the capabilities of PARC to simulate unsteady, transient, and advection-dominant systems. The extended model, referred to as PARCv2, is equipped with differential operators to model advection-reaction-diffusion equations, as well as a hybrid integral solver for stable, long-time predictions. PARCv2 is tested on both standard benchmark problems in fluid dynamics, namely Burgers and Navier-Stokes equations, and then applied to more complex shock-induced reaction problems in energetic materials. We evaluate the behavior of PARCv2 in comparison to other physics-informed and learning bias models and demonstrate its potential to model unsteady and advection-dominant dynamics regimes.

Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, Noseong Park

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Raynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification, solutions of those PDEs need to be evaluated at numerous points in the parameter space. While physics-informed neural networks (PINNs) have emerged as a new strong competitor as a surrogate, their usage in this scenario remains underexplored due to the inherent need for repetitive and time-consuming training. In this paper, we address this problem by proposing a novel extension, parameterized physics-informed neural networks (P$^2$INNs). P$^2$INNs enable modeling the solutions of parameterized PDEs via explicitly encoding a latent representation of PDE parameters. With the extensive empirical evaluation, we demonstrate that P$^2$INNs outperform the baselines both in accuracy and parameter efficiency on benchmark 1D and 2D parameterized PDEs and are also effective in overcoming the known “failure modes”.

Siqi Miao, Zhiyuan Lu, Mia Liu, Javier Duarte, Pan Li

This study introduces a novel transformer model optimized for large-scale point cloud processing in scientific domains such as high-energy physics (HEP) and astrophysics. Addressing the limitations of graph neural networks and standard transformers, our model integrates local inductive bias and achieves near-linear complexity with hardware-friendly regular operations. One contribution of this work is the quantitative analysis of the error-complexity tradeoff of various sparsification techniques for building efficient transformers. Our findings highlight the superiority of using locality-sensitive hashing (LSH), especially OR & AND-construction LSH, in kernel approximation for large-scale point cloud data with local inductive bias. Based on this finding, we propose LSH-based Efficient Point Transformer (**HEPT**), which combines E$^2$LSH with OR & AND constructions and is built upon regular computations. HEPT demonstrates remarkable performance on two critical yet time-consuming HEP tasks, significantly outperforming existing GNNs and transformers in accuracy and computational speed, marking a significant advancement in geometric deep learning and large-scale scientific data processing. Our code is available at https://github.com/Graph-COM/HEPT.

Miscellaneous Aspects of Machine Learning · Representation Learning

Zhengqi Pei, Anran Zhang, Shuhui Wang, Xiangyang Ji, Qingming Huang

Neural models are equivalent to dynamic systems from a physics-inspired view, implying that computation on neural networks can be interpreted as the dynamical interactions between neurons. However, existing work models neuronal interaction as a weight-based linear transformation, and the nonlinearity comes from the nonlinear activation functions, which leads to limited nonlinearity and data-fitting ability of the whole neural model. Inspired by Riemannian geometry, we interpret neural structures by projecting neurons onto the Riemannian neuronal state space and model neuronal interaction with Riemannian metric (${\it RieM}$), which provides a more efficient neural representation with higher parameter efficiency. With ${\it RieM}$, we further design a novel data-free neural compression mechanism that does not require additional fine-tuning with real data. Using backbones like ResNet and Vision Transformer, we conduct extensive experiments on datasets such as MNIST, CIFAR-100, ImageNet-1k, and COCO object detection. Empirical results show that, under equal compression rates and computational complexity, models compressed with ${\it RieM}$ achieve superior inference accuracy compared to existing data-free compression methods.

Applications · Physics

Zhuo Chen, Jacob McCarran, Esteban Vizcaino, Marin Soljačić, Di Luo

Partial differential equations (PDEs) are instrumental for modeling dynamical systems in science and engineering. The advent of neural networks has initiated a significant shift in tackling these complexities though challenges in accuracy persist, especially for initial value problems. In this paper, we introduce the *Time-Evolving Natural Gradient (TENG)*, generalizing time-dependent variational principles and optimization-based time integration, leveraging natural gradient optimization to obtain high accuracy in neural-network-based PDE solutions. Our comprehensive development includes algorithms like TENG-Euler and its high-order variants, such as TENG-Heun, tailored for enhanced precision and efficiency. TENG's effectiveness is further validated through its performance, surpassing current leading methods and achieving *machine precision* in step-by-step optimizations across a spectrum of PDEs, including the heat equation, Allen-Cahn equation, and Burgers' equation.

Applications · Language, Speech and Dialog

Pingchuan Ma, Johnson Tsun-Hsuan Wang, Minghao Guo, Zhiqing Sun, Josh Tenenbaum, Daniela Rus, Chuang Gan, Wojciech Matusik

Large Language Models have recently gained significant attention in scientific discovery for their extensive knowledge and advanced reasoning capabilities. However, they encounter challenges in effectively simulating observational feedback and grounding it with language to propel advancements in physical scientific discovery. Conversely, human scientists undertake scientific discovery by formulating hypotheses, conducting experiments, and revising theories through observational analysis. Inspired by this, we propose to enhance the knowledge-driven, abstract reasoning abilities of LLMs with the computational strength of simulations. We introduce Scientific Generative Agent (SGA), a bilevel optimization framework: LLMs act as knowledgeable and versatile thinkers, proposing scientific hypotheses and reason about discrete components, such as physics equations or molecule structures; meanwhile, simulations function as experimental platforms, providing observational feedback and optimizing via differentiability for continuous parts, such as physical parameters. We conduct extensive experiments to demonstrate our framework's efficacy in constitutive law discovery and molecular design, unveiling novel solutions that differ from conventional human expectations yet remain coherent upon analysis.

Bowen Jing, Bonnie Berger, Tommi Jaakkola

The biological functions of proteins often depend on dynamic structural ensembles. In this work, we develop a flow-based generative modeling approach for learning and sampling the conformational landscapes of proteins. We repurpose highly accurate single-state predictors such as AlphaFold and ESMFold and fine-tune them under a custom flow matching framework to obtain sequence-conditioned generative models of protein structure called AlphaFlow and ESMFlow. When trained and evaluated on the PDB, our method provides a superior combination of precision and diversity compared to AlphaFold with MSA subsampling. When further trained on ensembles from all-atom MD, our method accurately captures conformational flexibility, positional distributions, and higher-order ensemble observables for unseen proteins. Moreover, our method can diversify a static PDB structure with faster wall-clock convergence to certain equilibrium properties than replicate MD trajectories, demonstrating its potential as a proxy for expensive physics-based simulations. Code is available at https://github.com/bjing2016/alphaflow.

Applications · Chemistry and Drug Discovery

Nate Gruver, Anuroop Sriram, Andrea Madotto, Andrew Gordon Wilson, Larry Zitnick, Zachary Ulissi

We propose fine-tuning large language models for generation of stable materials. While unorthodox, fine-tuning large language models on text-encoded atomistic data is simple to implement yet reliable, with around 90\% of sampled structures obeying physical constraints on atom positions and charges. Using energy above hull calculations from both learned ML potentials and gold-standard DFT calculations, we show that our strongest model (fine-tuned LLaMA-2 70B) can generate materials predicted to be metastable at about twice the rate (49\% vs 28\%) of CDVAE, a competing diffusion model. Because of text prompting's inherent flexibility, our models can simultaneously be used for unconditional generation of stable material, infilling of partial structures and text-conditional generation. Finally, we show that language models' ability to capture key symmetries of crystal structures improves with model scale, suggesting that the biases of pretrained LLMs are surprisingly well-suited for atomistic data.

Applications · Computer Vision

Qinhong Zhou, Sunli Chen, Yisong Wang, Haozhe Xu, Weihua Du, Hongxin Zhang, Yilun Du, Joshua B Tenenbaum, Chuang Gan

Recent advances in high-fidelity virtual environments serve as one of the major driving forces for building intelligent embodied agents to perceive, reason and interact with the physical world. Typically, these environments remain unchanged unless agents interact with them. However, in real-world scenarios, agents might also face dynamically changing environments characterized by unexpected events and need to rapidly take action accordingly. To remedy this gap, we propose a new simulated embodied benchmark, called HAZARD, specifically designed to assess the decision-making abilities of embodied agents in dynamic situations. HAZARD consists of three unexpected disaster scenarios, including fire, flood, and wind, and specifically supports the utilization of large language models (LLMs) to assist common sense reasoning and decision-making. This benchmark enables us to evaluate autonomous agents' decision-making capabilities across various pipelines, including reinforcement learning (RL), rule-based, and search-based methods in dynamically changing environments. As a first step toward addressing this challenge using large language models, we further develop an LLM-based agent and perform an in-depth analysis of its promise and challenge of solving these challenging tasks. HAZARD is available at https://vis-www.cs.umass.edu/hazard/.

Applications

Paula Harder, Alex Hernandez-Garcia, Venkatesh Ramesh, Qidong Yang, Prasanna Sattigeri, Daniela Szwarcman, Campbell Watson, David Rolnick

The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by computational costs and, therefore, often generate coarse-resolution predictions. Statistical downscaling, including super-resolution methods from deep learning, can provide an efficient method of upsampling low-resolution data. However, despite achieving visually compelling results in some cases, such models frequently violate conservation laws when predicting physical variables. In order to conserve physical quantities, here we introduce methods that guarantee statistical constraints are satisfied by a deep learning downscaling model, while also improving their performance according to traditional metrics. We compare different constraining approaches and demonstrate their applicability across different neural architectures as well as a variety of climate and weather data sets. Besides enabling faster and more accurate climate predictions through downscaling, we also show that our novel methodologies can improve super-resolution for satellite data and natural images data sets.

Zhen Liu, Yao Feng, Yuliang Xiu, Weiyang Liu, Liam Paull, Michael J Black, Bernhard Schoelkopf

The creation of photorealistic virtual worlds requires the accurate modeling of 3D surface geometry for a wide range of objects. For this, meshes are appealing since they enable 1) fast physics-based rendering with realistic material and lighting, 2) physical simulation, and 3) are memory-efficient for modern graphics pipelines. Recent work on reconstructing and statistically modeling 3D shape, however, has critiqued meshes as being topologically inflexible. To capture a wide range of object shapes, any 3D representation must be able to model solid, watertight, shapes as well as thin, open, surfaces. Recent work has focused on the former, and methods for reconstructing open surfaces do not support fast reconstruction with material and lighting or unconditional generative modelling. Inspired by the observation that open surfaces can be seen as islands floating on watertight surfaces, we parametrize open surfaces by defining a manifold signed distance field on watertight templates. With this parametrization, we further develop a grid-based and differentiable representation that parametrizes both watertight and non-watertight meshes of arbitrary topology. Our new representation, called Ghost-on-the-Shell (G-Shell), enables two important applications: differentiable rasterization-based reconstruction from multiview images and generative modelling of non-watertight meshes. We empirically demonstrate that G-Shell achieves state-of-the-art performance on non-watertight mesh reconstruction and generation tasks, while also performing effectively for watertight meshes.