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Probabilistic Methods · Gaussian Processes

Oliver Hamelijnck, Arno Solin, Theodoros Damoulas

Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Applications

Qi Wang, Pu Ren, Hao Zhou, Xin-Yang Liu, Zhiwen Deng, Yi Zhang, Zeruizhi Cheng, Hongsheng Liu, Zidong Wang, Jian-Xun Wang 等

When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently, machine learning has been increasingly utilized to solve PDE problems, but they often encounter challenges related to interpretability, generalizability, and strong dependency on rich labeled data. Hence, we introduce a new PDE-Preserved Coarse Correction Network (P$^2$C$^2$Net) to efficiently solve spatiotemporal PDE problems on coarse mesh grids in small data regimes. The model consists of two synergistic modules: (1) a trainable PDE block that learns to update the coarse solution (i.e., the system state), based on a high-order numerical scheme with boundary condition encoding, and (2) a neural network block that consistently corrects the solution on the fly. In particular, we propose a learnable symmetric Conv filter, with weights shared over the entire model, to accurately estimate the spatial derivatives of PDE based on the neural-corrected system state. The resulting physics-encoded model is capable of handling limited training data (e.g., 3--5 trajectories) and accelerates the prediction of PDE solutions on coarse spatiotemporal grids while maintaining a high accuracy. P$^2$C$^2$Net achieves consistent state-of-the-art performance with over 50\% gain (e.g., in terms of relative prediction error) across four datasets covering complex reaction-diffusion processes and turbulent flows.

Physical Models

Benedikt Alkin, Andreas Fürst, Simon Schmid, Lukas Gruber, Markus Holzleitner, Johannes Brandstetter

Neural operators, serving as physics surrogate models, have recently gained increased interest. With ever increasing problem complexity, the natural question arises: what is an efficient way to scale neural operators to larger and more complex simulations - most importantly by taking into account different types of simulation datasets. This is of special interest since, akin to their numerical counterparts, different techniques are used across applications, even if the underlying dynamics of the systems are similar. Whereas the flexibility of transformers has enabled unified architectures across domains, neural operators mostly follow a problem specific design, where GNNs are commonly used for Lagrangian simulations and grid-based models predominate Eulerian simulations. We introduce Universal Physics Transformers (UPTs), an efficient and unified learning paradigm for a wide range of spatio-temporal problems. UPTs operate without grid- or particle-based latent structures, enabling flexibility and scalability across meshes and particles. UPTs efficiently propagate dynamics in the latent space, emphasized by inverse encoding and decoding techniques. Finally, UPTs allow for queries of the latent space representation at any point in space-time. We demonstrate diverse applicability and efficacy of UPTs in mesh-based fluid simulations, and steady-state Reynolds averaged Navier-Stokes simulations, and Lagrangian-based dynamics.

Generative Models · Diffusion models

Max Jiang, Yijing Bai, Andre Cornman, Christopher Davis, XIUKUN HUANG, Hong Jeon, Sakshum Kulshrestha, John Lambert, Shuangyu Li, Xuanyu Zhou 等

Simulation with realistic and interactive agents represents a key task for autonomous vehicle (AV) software development in order to test AV performance in prescribed, often long-tail scenarios. In this work, we propose SceneDiffuser, a scene-level diffusion prior for traffic simulation. We present a singular framework that unifies two key stages of simulation: scene initialization and scene rollout. Scene initialization refers to generating the initial layout for the traffic in a scene, and scene rollout refers to closed-loop simulation for the behaviors of the agents. While diffusion has been demonstrated to be effective in learning realistic, multimodal agent distributions, two open challenges remain: controllability and closed-loop inference efficiency and realism. To this end, to address controllability challenges, we propose generalized hard constraints, a generalized inference-time constraint mechanism that is simple yet effective. To improve closed-loop inference quality and efficiency, we propose amortized diffusion, a novel diffusion denoising paradigm that amortizes the physical cost of denoising over future simulation rollout steps, reducing the cost of per physical rollout step to a single denoising function evaluation, while dramatically reducing closed-loop errors. We demonstrate the effectiveness of our approach on the Waymo Open Dataset, where we are able to generate distributionally realistic scenes, while obtaining competitive performance in the Sim Agents Challenge, surpassing the state-of-the-art in many realism attributes.

Computational Biology

David Brookes, Jakub Otwinowski, Sam Sinai

Fitness functions map large combinatorial spaces of biological sequences to properties of interest. Inferring these multimodal functions from experimental data is a central task in modern protein engineering. Global epistasis models are an effective and physically-grounded class of models for estimating fitness functions from observed data. These models assume that a sparse latent function is transformed by a monotonic nonlinearity to emit measurable fitness. Here we demonstrate that minimizing supervised contrastive loss functions, such as the Bradley-Terry loss, is a simple and flexible technique for extracting the sparse latent function implied by global epistasis. We argue by way of a fitness-epistasis uncertainty principle that the nonlinearities in global epistasis models can produce observed fitness functions that do not admit sparse representations, and thus may be inefficient to learn from observations when using a Mean Squared Error (MSE) loss (a common practice). We show that contrastive losses are able to accurately estimate a ranking function from limited data even in regimes where MSE is ineffective and validate the practical utility of this insight by demonstrating that contrastive loss functions result in consistently improved performance on empirical benchmark tasks.

Probabilistic Methods · Bayesian Models and Methods

Rafael Oliveira, Dino Sejdinovic, David Howard, Edwin Bonilla

The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current machine learning approaches, however, mostly rely on rerunning simulations over a fixed set of designs available in the observed data, potentially neglecting informative correlations across the design space and requiring a large amount of simulations. Instead, we consider the calibration process from the perspective of Bayesian adaptive experimental design and propose a data-efficient algorithm to run maximally informative simulations within a batch-sequential process. At each round, the algorithm jointly estimates the parameters posterior distribution and optimal designs by maximising a variational lower bound of the expected information gain. The simulator is modelled as a sample from a Gaussian process, which allows us to correlate simulations and real data with the unknown calibration parameters. We show the benefits of our method when compared to related approaches across synthetic and real-data problems.

Robotics

Maximilian Stölzle, Cosimo Della Santina

Even though a variety of methods have been proposed in the literature, efficient and effective latent-space control (i.e., control in a learned low-dimensional space) of physical systems remains an open challenge.We argue that a promising avenue is to leverage powerful and well-understood closed-form strategies from control theory literature in combination with learned dynamics, such as potential-energy shaping.We identify three fundamental shortcomings in existing latent-space models that have so far prevented this powerful combination: (i) they lack the mathematical structure of a physical system, (ii) they do not inherently conserve the stability properties of the real systems, (iii) these methods do not have an invertible mapping between input and latent-space forcing.This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it possesses well-defined potential and kinetic energy terms. Then, (ii) we provide formal proof of global Input-to-State stability using Lyapunov arguments.Moving to the experimental side, we demonstrate that CON reaches SoA performance when learning complex nonlinear dynamics of mechanical systems directly from images.An additional methodological innovation contributing to achieving this third goal is an approximated closed-form solution for efficient integration of network dynamics, which eases efficient training.We tackle (iii) by approximating the forcing-to-input mapping with a decoder that is trained to reconstruct the input based on the encoded latent space force.Finally, we leverage these three properties and show that they enable latent-space control. We use an integral-saturated PID with potential force compensation and demonstrate high-quality performance on a soft robot using raw pixels as the only feedback information.

Physical Models · Physics

Navami Kairanda, Marc Habermann, Christian Theobalt, Vladislav Golyanik

Despite existing 3D cloth simulators producing realistic results, they predominantly operate on discrete surface representations (e.g. points and meshes) with a fixed spatial resolution, which often leads to large memory consumption and resolution-dependent simulations. Moreover, back-propagating gradients through the existing solvers is difficult and they hence cannot be easily integrated into modern neural architectures. In response, this paper re-thinks physically plausible cloth simulation: We propose NeuralClothSim, i.e., a new quasistatic cloth simulator using thin shells, in which surface deformation is encoded in neural network weights in form of a neural field. Our memory-efficient solver operates on a new continuous coordinate-based surface representation called neural deformation fields (NDFs); it supervises NDF equilibria with the laws of the non-linear Kirchhoff-Love shell theory with a non-linear anisotropic material model. NDFs are adaptive: They 1) allocate their capacity to the deformation details and 2) allow surface state queries at arbitrary spatial resolutions without re-training. We show how to train NeuralClothSim while imposing hard boundary conditions and demonstrate multiple applications, such as material interpolation and simulation editing. The experimental results highlight the effectiveness of our continuous neural formulation.

Physical Models · Physics

Viktor Zaverkin, Francesco Alesiani, Takashi Maruyama, Federico Errica, Henrik Christiansen, Makoto Takamoto, Nicolas Weber, Mathias Niepert

The ability to perform fast and accurate atomistic simulations is crucial for advancing the chemical sciences. By learning from high-quality data, machine-learned interatomic potentials achieve accuracy on par with ab initio and first-principles methods at a fraction of their computational cost. The success of machine-learned interatomic potentials arises from integrating inductive biases such as equivariance to group actions on an atomic system, e.g., equivariance to rotations and reflections. In particular, the field has notably advanced with the emergence of equivariant message passing. Most of these models represent an atomic system using spherical tensors, tensor products of which require complicated numerical coefficients and can be computationally demanding. Cartesian tensors offer a promising alternative, though state-of-the-art methods lack flexibility in message-passing mechanisms, restricting their architectures and expressive power. This work explores higher-rank irreducible Cartesian tensors to address these limitations. We integrate irreducible Cartesian tensor products into message-passing neural networks and prove the equivariance and traceless property of the resulting layers. Through empirical evaluations on various benchmark data sets, we consistently observe on-par or better performance than that of state-of-the-art spherical and Cartesian models.

Guanghao Wei, Yining Huang, Chenru Duan, Yue Song, Yuanqi Du

Recent progress of deep generative models in the vision and language domain has stimulated significant interest in more structured data generation such as molecules. However, beyond generating new random molecules, efficient exploration and a comprehensive understanding of the vast chemical space are of great importance to molecular science and applications in drug design and materials discovery.In this paper, we propose a new framework, ChemFlow, to traverse chemical space through navigating the latent space learned by molecule generative models through flows. We introduce a dynamical system perspective that formulates the problem as learning a vector field that transports the mass of the molecular distribution to the region with desired molecular properties or structure diversity. Under this framework, we unify previous approaches on molecule latent space traversal and optimization and propose alternative competing methods incorporating different physical priors. We validate the efficacy of ChemFlow on molecule manipulation and single- and multi-objective molecule optimization tasks under both supervised and unsupervised molecular discovery settings.Codes and demos are publicly available on GitHub at [https://github.com/garywei944/ChemFlow](https://github.com/garywei944/ChemFlow).

Miscellaneous Aspects of Machine Learning · General Machine Learning Techniques

Zekun Shi, Zheyuan Hu, Min Lin, Kenji Kawaguchi

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to $\mathcal{O}(d^{k})$ scaling of the derivative tensor size and the $\mathcal{O}(2^{k-1}L)$ scaling in the computation graph, where $d$ is the dimension of the domain, $L$ is the number of ops in the forward computation graph, and $k$ is the derivative order. In previous works, the polynomial scaling in $d$ was addressed by amortizing the computation over the optimization process via randomization. Separately, the exponential scaling in $k$ for univariate functions ($d=1$) was addressed with high-order auto-differentiation (AD). In this work, we show how to efficiently perform arbitrary contraction of the derivative tensor of arbitrary order for multivariate functions, by properly constructing the input tangents to univariate high-order AD, which can be used to efficiently randomize any differential operator. When applied to Physics-Informed Neural Networks (PINNs), our method provides >1000$\times$ speed-up and >30$\times$ memory reduction over randomization with first-order AD, and we can now solve 1-million-dimensional PDEs in 8 minutes on a single NVIDIA A100 GPU. This work opens the possibility of using high-order differential operators in large-scale problems.

Reinforcement Learning · Everything Else

Minjong Yoo, Jinwoo Jang, Wei-Jin Park, Honguk Woo

This study presents an Exploratory Retrieval-Augmented Planning (ExRAP) framework, designed to tackle continual instruction following tasks of embodied agents in dynamic, non-stationary environments. The framework enhances Large Language Models' (LLMs) embodied reasoning capabilities by efficiently exploring the physical environment and establishing the environmental context memory, thereby effectively grounding the task planning process in time-varying environment contexts. In ExRAP, given multiple continual instruction following tasks, each instruction is decomposed into queries on the environmental context memory and task executions conditioned on the query results. To efficiently handle these multiple tasks that are performed continuously and simultaneously, we implement an exploration-integrated task planning scheme by incorporating the information-based exploration into the LLM-based planning process. Combined with memory-augmented query evaluation, this integrated scheme not only allows for a better balance between the validity of the environmental context memory and the load of environment exploration, but also improves overall task performance. Furthermore, we devise a temporal consistency refinement scheme for query evaluation to address the inherent decay of knowledge in the memory. Through experiments with VirtualHome, ALFRED, and CARLA, our approach demonstrates robustness against a variety of embodied instruction following scenarios involving different instruction scales and types, and non-stationarity degrees, and it consistently outperforms other state-of-the-art LLM-based task planning approaches in terms of both goal success rate and execution efficiency.

Physical Models · Physics

Arya Grayeli, Atharva Sehgal, Omar Costilla Reyes, Miles Cranmer, Swarat Chaudhuri

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LASR can be used to discover a new and powerful scaling law for LLMs.

Generative Models · Diffusion models

Quentin Leboutet, Nina Wiedemann, zhipeng cai, Michael Paulitsch, Kai Yuan

Providing functionality through articulation and interaction with objects is a key objective in 3D generation. We introduce MIDGArD (Modular Interpretable Diffusion over Graphs for Articulated Designs), a novel diffusion-based framework for articulated 3D asset generation. MIDGArD improves over foundational work in the field by enhancing quality, consistency, and controllability in the generation process. This is achieved through MIDGArD's modular approach that separates the problem into two primary components: structure generation and shape generation. The structure generation module of MIDGArD aims at producing coherent articulation features from noisy or incomplete inputs. It acts on the object's structural and kinematic attributes, represented as features of a graph that are being progressively denoised to issue coherent and interpretable articulation solutions. This denoised graph then serves as an advanced conditioning mechanism for the shape generation module, a 3D generative model that populates each link of the articulated structure with consistent 3D meshes. Experiments show the superiority of MIDGArD on the quality, consistency, and interpretability of the generated assets. Importantly, the generated models are fully simulatable, i.e., can be seamlessly integrated into standard physics engines such as MuJoCo, broadening MIDGArD's applicability to fields such as digital content creation, meta realities, and robotics.

Keji He, Kehan Chen, Jiawang Bai, Yan Huang, Qi Wu, Shu-Tao Xia, Liang Wang

Vision-and-Language Navigation (VLN) requires an agent to dynamically explore environments following natural language.The VLN agent, closely integrated into daily lives, poses a substantial threat to the security of privacy and property upon the occurrence of malicious behavior.However, this serious issue has long been overlooked.In this paper, we pioneer the exploration of an object-aware backdoored VLN, achieved by implanting object-aware backdoors during the training phase. Tailored to the unique VLN nature of cross-modality and continuous decision-making, we propose a novel backdoored VLN paradigm: IPR Backdoor. This enables the agent to act in abnormal behavior once encountering the object triggers during language-guided navigation in unseen environments, thereby executing an attack on the target scene.Experiments demonstrate the effectiveness of our method in both physical and digital spaces across different VLN agents, as well as its robustness to various visual and textual variations. Additionally, our method also well ensures navigation performance in normal scenarios with remarkable stealthiness.

Physical Models

Sebastian Zeng, Florian Graf, Martin Uray, Stefan Huber, Roland Kwitt

We consider the problem of learning the dynamics in the topology of time-evolving point clouds, the prevalent spatiotemporal model for systems exhibiting collective behavior, such as swarms of insects and birds or particles in physics. In such systems, patterns emerge from (local) interactions among self-propelled entities. While several well-understood governing equations for motion and interaction exist, they are notoriously difficult to fit to data, as most prior work requires knowledge about individual motion trajectories, i.e., a requirement that is challenging to satisfy with an increasing number of entities. To evade such confounding factors, we investigate collective behavior from a _topological perspective_, but instead of summarizing entire observation sequences (as done previously), we propose learning a latent dynamical model from topological features _per time point_. The latter is then used to formulate a downstream regression task to predict the parametrization of some a priori specified governing equation. We implement this idea based on a latent ODE learned from vectorized (static) persistence diagrams and show that a combination of recent stability results for persistent homology justifies this modeling choice. Various (ablation) experiments not only demonstrate the relevance of each model component but provide compelling empirical evidence that our proposed model -- _Neural Persistence Dynamics_ -- substantially outperforms the state-of-the-art across a diverse set of parameter regression tasks.

Deep Learning · Algorithms

Mohammad Mahmudul Alam, Alexander Oberle, Edward Raff, Stella Biderman, Tim Oates, James Holt

Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ are 'bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of this binding operation, along with an inverse operation, allowing one to construct symbolic-style manipulations over real-valued vectors. Most VSAs were developed before deep learning and automatic differentiation became popular and instead focused on efficacy in hand-designed systems. In this work, we introduce the Hadamard-derived linear Binding (HLB), which is designed to have favorable computational efficiency, and efficacy in classic VSA tasks, and perform well in differentiable systems.

Computer Vision

Zhongpai Gao, Benjamin Planche, Meng Zheng, Xiao Chen, Terrence Chen, Ziyan Wu

Digitally reconstructed radiographs (DRRs) are simulated 2D X-ray images generated from 3D CT volumes, widely used in preoperative settings but limited in intraoperative applications due to computational bottlenecks. Physics-based Monte Carlo simulations provide accurate representations but are extremely computationally intensity. Analytical DRR renderers are much more efficient, but at the price of ignoring anisotropic X-ray image formation phenomena such as Compton scattering. We propose a novel approach that balances realistic physics-inspired X-ray simulation with efficient, differentiable DRR generation using 3D Gaussian splatting (3DGS). Our direction-disentangled 3DGS (DDGS) method decomposes the radiosity contribution into isotropic and direction-dependent components, able to approximate complex anisotropic interactions without complex runtime simulations. Additionally, we adapt the 3DGS initialization to account for tomography data properties, enhancing accuracy and efficiency. Our method outperforms state-of-the-art techniques in image accuracy and inference speed, demonstrating its potential for intraoperative applications and inverse problems like pose registration.

Computer Vision · Video Generation

Antonio Montanaro, Luca Savant Aira, Emanuele Aiello, Diego Valsesia, Enrico Magli

Generating videos with realistic and physically plausible motion is one of the main recent challenges in computer vision. While diffusion models are achieving compelling results in image generation, video diffusion models are limited by heavy training and huge models, resulting in videos that are still biased to the training dataset. In this work we propose MotionCraft, a new zero-shot video generator to craft physics-based and realistic videos. MotionCraft is able to warp the noise latent space of an image diffusion model, such as Stable Diffusion, by applying an optical flow derived from a physics simulation. We show that warping the noise latent space results in coherent application of the desired motion while allowing the model to generate missing elements consistent with the scene evolution, which would otherwise result in artefacts or missing content if the flow was applied in the pixel space.We compare our method with the state-of-the-art Text2Video-Zero reporting qualitative and quantitative improvements, demonstrating the effectiveness of our approach to generate videos with finely-prescribed complex motion dynamics.

Deep Learning · Robustness

Zhi Cheng, Zhanhao Hu, Yuqiu Liu, Jianmin Li, Hang Su, Xiaolin Hu

Many studies have proposed attack methods to generate adversarial patterns for evading pedestrian detection, alarming the computer vision community about the need for more attention to the robustness of detectors. However, adversarial patterns optimized by these methods commonly have limited performance at medium to long distances in the physical world. To overcome this limitation, we identify two main challenges. First, in existing methods, there is commonly an appearance gap between simulated distant adversarial patterns and their physical world counterparts, leading to incorrect optimization. Second, there exists a conflict between adversarial losses at different distances, which causes difficulties in optimization. To overcome these challenges, we introduce a Full Distance Attack (FDA) method. Our physical world experiments demonstrate the effectiveness of our FDA patterns across various detection models like YOLOv5, Deformable-DETR, and Mask RCNN. Codes available at https://github.com/zhicheng2T0/Full-Distance-Attack.git