Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We develop a scalable framework for differentiable physics that can support a large number of objects and their interactions. To accommodate objects with arbitrary geometry and topology, we adopt meshes as our representation and leverage the sparsity of contacts for scalable differentiable collision handling. Collisions are resolved in localized regions to minimize the number of optimization variables even when the number of simulated objects is high. We further accelerate implicit differentiation of optimization with nonlinear constraints. Experiments demonstrate that the presented framework requires up to two orders of magnitude less memory and computation in comparison to recent particle-based methods. We further validate the approach on inverse problems and control scenarios, where it outperforms derivative-free and model-free baselines by at least an order of magnitude.
Center for Data Science, Zhejiang University（浙江大学数据科学中心）；Information Hub, The Hong Kong University of Science and Technology（香港科技大学信息枢纽）；College of Computer Science, Zhejiang University（浙江大学计算机科学与技术学院）
Data imputation has been extensively explored to solve the missing data problem. The dramatically increasing volume of incomplete data makes the imputation models computationally infeasible in many real-life applications. In this paper, we propose an effective scalable imputation system named SCIS to significantly speed up the training of the differentiable generative adversarial imputation models under accuracy-guarantees for large-scale incomplete data. SCIS consists of two modules, differentiable imputation modeling (DIM) and sample size estimation (SSE). DIM leverages a new masking Sinkhor…
University of Konstanz（康斯坦茨大学）；University of Salzburg（萨尔茨堡大学）；University of Frankfurt（法兰克福大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we propose differentiable sorting networks by relaxing their pairwise conditional swap operations. To address the problems of vanishing gradients and extensive blurring that arise with larger numbers of layers, we propose mapping activations to regions with moderate gradients. We consider odd-even as well as bitonic sorting networks, which outperform existing rel…
Deep learning models are often not easily adaptable to new tasks and require task-specific adjustments. The differentiable neural computer (DNC), a memory-augmented neural network, is designed as a general problem solver which can be used in a wide range of tasks. But in reality, it is hard to apply this model to new tasks. We analyze the DNC and identify possible improvements within the application of question answering. This motivates a more robust and scalable DNC (rsDNC). The objective precondition is to keep the general character of this model intact while making its application more reli…
Learning efficient and interpretable policies has been a challenging task in reinforcement learning (RL), particularly in the visual RL setting with complex scenes. While neural networks have achieved competitive performance, the resulting policies are often over-parameterized black boxes that are difficult to interpret and deploy efficiently. More recent symbolic RL frameworks have shown that high-level domain-specific programming logic can be designed to handle both policy learning and symbolic planning. However, these approaches rely on coded primitives with little feature learning, and whe…
Amazon（亚马逊）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Facebook AI Research（Facebook人工智能研究院）；Stanford University（斯坦福大学）
A key challenge with machine learning approaches for ranking is the gap between the performance metrics of interest and the surrogate loss functions that can be optimized with gradient-based methods. This gap arises because ranking metrics typically involve a sorting operation which is not differentiable w.r.t. the model parameters. Prior works have proposed surrogates that are loosely related to ranking metrics or simple smoothed versions thereof, and often fail to scale to real-world applications. We propose PiRank, a new class of differentiable surrogates for ranking, which employ a continu…
Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）；University of Maryland（马里兰大学）
We formulate the first differentiable analog quantum computing framework with a specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum comp…
We propose topology-aware feature partitioning into $k$ disjoint partitions for given scene features as a method for object-centric representation learning. To this end, we propose to use minimum $s$-$t$ graph cuts as a partitioning method which is represented as a linear program. The method is topologically aware since it explicitly encodes neighborhood relationships in the image graph. To solve the graph cuts our solution relies on an efficient, scalable, and differentiable quadratic programming approximation. Optimizations specific to cut problems allow us to solve the quadratic programs an…
Nanyang Technological University（南洋理工大学）；National University of Singapore（新加坡国立大学）
We propose $\mathcal{T}$ruth $\mathcal{T}$able net ($\mathcal{TT}$net), a novel Convolutional Neural Network (CNN) architecture that addresses, by design, the open challenges of interpretability, formal verification, and logic gate conversion. $\mathcal{TT}$net is built using CNNs' filters that are equivalent to tractable truth tables and that we call Learning Truth Table (LTT) blocks. The dual form of LTT blocks allows the truth tables to be easily trained with gradient descent and makes these CNNs easy to interpret, verify and infer. Specifically, $\mathcal{TT}$net is a deep CNN model that c…
Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization
Research Center for Mathematical Engineering, Chiba Institute of Technology（千叶工业大学数学工程研究中心）；International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo（东京大学国际神经智能研究中心（WPI-IRCN））；NEC Corporation（日本电气公司）
University of Utah（犹他大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state transitions, we focus on implicit state transitions defined via function minimization. Implicit state transitions appear in implicit numerical integration methods, which offer the benefits of large time steps and excellent numerical stability, but require a special treatment to achieve differentiability due to the absence of an explicit differentiable forward pass. In …
Memory-augmented neural networks (MANNs) provide better inference performance in many tasks with the help of an external memory. The recently developed differentiable neural computer (DNC) is a MANN that has been shown to outperform in representing complicated data structures and learning long-term dependencies. DNC's higher performance is derived from new history-based attention mechanisms in addition to the previously used content-based attention mechanisms. History-based mechanisms require a variety of new compute primitives and state memories, which are not supported by existing neural net…
University of Southern California（南加州大学）；Department of Computer Science, University of Southern California（南加州大学计算机科学系）
While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture called Differentiable Physics-informed Graph Networks (DPGN) to incorporate implicit physics knowledge which is given from domain experts by informing it in latent space. Using the concept of DPGN, we demonstrate that climate prediction tasks are significantly improved. Besides the e…
Deep Forest Sciences Inc.（深林科学公司）；Carnegie Mellon University（卡内基梅隆大学）
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly growing literature of differentiable physics techniques and highlight methods for parameter estimation, learning representations, solving differential equations, and developing what we call scientific foundation models using data and inductive priors. We argue that differentiable physics offers a new paradigm for modeling physical phenomena by combining class…
University of Maryland, College Park（马里兰大学帕克分校）；NVIDIA（英伟达）
We introduce a novel differentiable hybrid traffic simulator, which simulates traffic using a hybrid model of both macroscopic and microscopic models and can be directly integrated into a neural network for traffic control and flow optimization. This is the first differentiable traffic simulator for macroscopic and hybrid models that can compute gradients for traffic states across time steps and inhomogeneous lanes. To compute the gradient flow between two types of traffic models in a hybrid framework, we present a novel intermediate conversion component that bridges the lanes in a differentia…
Texas A&M University（德克萨斯农工大学）；University of Florida（佛罗里达大学）
In this paper, we study the problem of learning probabilistic logical rules for inductive and interpretable link prediction. Despite the importance of inductive link prediction, most previous works focused on transductive link prediction and cannot manage previously unseen entities. Moreover, they are black-box models that are not easily explainable for humans. We propose DRUM, a scalable and differentiable approach for mining first-order logical rules from knowledge graphs which resolves these problems. We motivate our method by making a connection between learning confidence scores for each …
Massachusetts Institute of Technology（麻省理工学院）；Arizona State University（亚利桑那州立大学）；Adobe（Adobe公司）；Mayo Clinic（梅奥诊所）；Alix School of Science and Medicine（艾利克斯科学与医学院）
We introduce DeepABM, a framework for agent-based modeling that leverages geometric message passing of graph neural networks for simulating action and interactions over large agent populations. Using DeepABM allows scaling simulations to large agent populations in real-time and running them efficiently on GPU architectures. To demonstrate the effectiveness of DeepABM, we build DeepABM-COVID simulator to provide support for various non-pharmaceutical interventions (quarantine, exposure notification, vaccination, testing) for the COVID-19 pandemic, and can scale to populations of representative …
University of Rochester（罗切斯特大学）；UC San Diego（加州大学圣地亚哥分校）；MIT（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Differentiable physics has recently been shown as a powerful tool for solving soft-body manipulation tasks. However, the differentiable physics solver often gets stuck when the initial contact points of the end effectors are sub-optimal or when performing multi-stage tasks that require contact point switching, which often leads to local minima. To address this challenge, we propose a contact point discovery approach (CPDeform) that guides the stand-alone differentiable physics solver to deform various soft-body plasticines. The key idea of our approach is to integrate optimal transport-based c…
Physics-informed learning has shown to have a better generalization than learning without physical priors. However, training physics-informed deep neural networks requires some aspect of physical simulations to be written in a differentiable manner. Unfortunately, some operations and functionals commonly used in physical simulations are scattered, hard to integrate, and lack higher order derivatives which are needed in physical simulations. In this work, we present $ξ$-torch, a library of differentiable functionals for scientific simulations. Example functionals are a root finder and an initia…
University of Leeds（利兹大学）；University of Edinburgh（爱丁堡大学）；Peking University（北京大学）
Differentiable physics modeling combines physics models with gradient-based learning to provide model explicability and data efficiency. It has been used to learn dynamics, solve inverse problems and facilitate design, and is at its inception of impact. Current successes have concentrated on general physics models such as rigid bodies, deformable sheets, etc., assuming relatively simple structures and forces. Their granularity is intrinsically coarse and therefore incapable of modelling complex physical phenomena. Fine-grained models are still to be developed to incorporate sophisticated mater…
We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system and its parameters, we modularize the design of our engine using a discrete form of the governing equations of motion, similar to a traditional physics engine. We further reduce the dimension from 3D to 1D for each module, which allows efficient learning of system parameters using linear regression. As a side benefit, the regression parameters correspond to physical quantities, such as spring stiffness…
UC San Diego（加州大学圣迭戈分校）；MIT（麻省理工学院）；Peking University（北京大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）
Simulated virtual environments serve as one of the main driving forces behind developing and evaluating skill learning algorithms. However, existing environments typically only simulate rigid body physics. Additionally, the simulation process usually does not provide gradients that might be useful for planning and control optimizations. We introduce a new differentiable physics benchmark called PasticineLab, which includes a diverse collection of soft body manipulation tasks. In each task, the agent uses manipulators to deform the plasticine into the desired configuration. The underlying physi…
Learned multiphysics inversion with differentiable programming and machine learning
Georgia Institute of Technology（佐治亚理工学院）；Rice University（莱斯大学）；University Medical Center Utrecht（乌得勒支大学医学中心）；Microsoft（微软）；SINTEF Digital（挪威科技工业研究院数字研究所）；Imperial College London（帝国理工学院）
In recent years, an increasing amount of work has focused on differentiable physics simulation and has produced a set of open source projects such as Tiny Differentiable Simulator, Nimble Physics, diffTaichi, Brax, Warp, Dojo and DiffCoSim. By making physics simulations end-to-end differentiable, we can perform gradient-based optimization and learning tasks. A majority of differentiable simulators consider collisions and contacts between objects, but they use different contact models for differentiability. In this paper, we overview four kinds of differentiable contact formulations - linear co…
Technical University of Munich（慕尼黑工业大学）；Intel Labs（英特尔实验室）
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations (PDEs) with many degrees of freedom. Existing methods that aim to control the dynamics of such systems are typically limited to relatively short time frames or a small number of interaction parameters. We present a novel hierarchical predictor-corrector scheme which enables neural networks to learn to understand and control complex nonlinear physical systems over…
We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system \emph{and} its parameters, we modularize the design of our engine using a discrete form of the governing equations of motion, similar to a traditional physics engine. We further reduce the dimension from 3D to 1D for each module, which allows efficient learning of system parameters using linear regression. The regression parameters correspond to physical quantities, such as spring stiffness or the mass…
We present differentiable predictive control (DPC), a method for learning constrained neural control policies for linear systems with probabilistic performance guarantees. We employ automatic differentiation to obtain direct policy gradients by backpropagating the model predictive control (MPC) loss function and constraints penalties through a differentiable closed-loop system dynamics model. We demonstrate that the proposed method can learn parametric constrained control policies to stabilize systems with unstable dynamics, track time-varying references, and satisfy nonlinear state and input …
Carnegie Mellon University（卡内基梅隆大学）；UC San Diego（加州大学圣地亚哥分校）；MIT（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
We consider the problem of sequential robotic manipulation of deformable objects using tools. Previous works have shown that differentiable physics simulators provide gradients to the environment state and help trajectory optimization to converge orders of magnitude faster than model-free reinforcement learning algorithms for deformable object manipulation. However, such gradient-based trajectory optimization typically requires access to the full simulator states and can only solve short-horizon, single-skill tasks due to local optima. In this work, we propose a novel framework, named DiffSkil…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；HKU（香港大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；MIT BCS（麻省理工学院脑与认知科学系）；CBMM（麻省理工学院大脑、心智与机器研究中心）
In this work, we propose a unified framework, called Visual Reasoning with Differ-entiable Physics (VRDP), that can jointly learn visual concepts and infer physics models of objects and their interactions from videos and language. This is achieved by seamlessly integrating three components: a visual perception module, a concept learner, and a differentiable physics engine. The visual perception module parses each video frame into object-centric trajectories and represents them as latent scene representations. The concept learner grounds visual concepts (e.g., color, shape, and material) from t…
We present a fast and feature-complete differentiable physics engine, Nimble (nimblephysics.org), that supports Lagrangian dynamics and hard contact constraints for articulated rigid body simulation. Our differentiable physics engine offers a complete set of features that are typically only available in non-differentiable physics simulators commonly used by robotics applications. We solve contact constraints precisely using linear complementarity problems (LCPs). We present efficient and novel analytical gradients through the LCP formulation of inelastic contact that exploit the sparsity of th…
DiffGen: Robot Demonstration Generation via Differentiable Physics Simulation, Differentiable Rendering, and Vision-Language Model
University of Chinese Academy of Sciences（中国科学院大学）；Shanghai Jiao Tong University（上海交通大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
Massachusetts Institute of Technology（麻省理工学院）；Tsinghua University（清华大学）
Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and therefore they are significantly more computationally expe…
We present a differentiable greenhouse simulation model based on physical processes whose parameters can be obtained by training from real data. The physics-based simulation model is fully interpretable and is able to do state prediction for both climate and crop dynamics in the greenhouse over very a long time horizon. The model works by constructing a system of linear differential equations and solving them to obtain the next state. We propose a procedure to solve the differential equations, handle the problem of missing unobservable states in the data, and train the model efficiently. Our e…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
In recent years, fully differentiable rigid body physics simulators have been developed, which can be used to simulate a wide range of robotic systems. In the context of reinforcement learning for control, these simulators theoretically allow algorithms to be applied directly to analytic gradients of the reward function. However, to date, these gradients have proved extremely challenging to use, and are outclassed by algorithms using no gradient information at all. In this work we present a novel algorithm, cross entropy analytic policy gradients, that is able to leverage these gradients to ou…
NeuralOGCM: Differentiable Ocean Modeling with Learnable Physics
Tsinghua University, Beijing, China（清华大学）；University of Science and Technology of China, Hefei, China（中国科学技术大学）；The Chinese University of Hong Kong, Hong Kong, China（香港中文大学）；Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China（香港科学与技术大学（广州））
Paul Scherrer Institute（保罗·谢勒研究所）；Argonne National Laboratory（阿贡国家实验室）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Universität Hamburg（汉堡大学）；Rutgers University（罗格斯大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；Massachusetts Institute of Technology（麻省理工学院）
The computational cost for high energy physics detector simulation in future experimental facilities is going to exceed the current available resources. To overcome this challenge, new ideas on surrogate models using machine learning methods are being explored to replace computationally expensive components. Additionally, differentiable programming has been proposed as a complementary approach, providing controllable and scalable simulation routines. In this document, new and ongoing efforts for surrogate models and differential programming applied to detector simulation are discussed in the c…
Ergodic LLC（Ergodic有限责任公司）；University of Michigan（密歇根大学）
Plasma supports collective modes and particle-wave interactions that leads to complex behavior in inertial fusion energy applications. While plasma can sometimes be modeled as a charged fluid, a kinetic description is useful towards the study of nonlinear effects in the higher dimensional momentum-position phase-space that describes the full complexity of plasma dynamics. We create a differentiable solver for the plasma kinetics 3D partial-differential-equation and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks th…
Carnegie Mellon University（卡内基梅隆大学）；Argonne National Laboratory（阿贡国家实验室）
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers' turbulence. We consider the 1D Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models acro…
Sea AI Lab（Sea人工智能实验室）；National University of Singapore（新加坡国立大学）
Existing imitation learning (IL) methods such as inverse reinforcement learning (IRL) usually have a double-loop training process, alternating between learning a reward function and a policy and tend to suffer long training time and high variance. In this work, we identify the benefits of differentiable physics simulators and propose a new IL method, i.e., Imitation Learning via Differentiable Physics (ILD), which gets rid of the double-loop design and achieves significant improvements in final performance, convergence speed, and stability. The proposed ILD incorporates the differentiable phys…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Differentiable physics is a powerful tool in computer vision and robotics for scene understanding and reasoning about interactions. Existing approaches have frequently been limited to objects with simple shape or shapes that are known in advance. In this paper, we propose a novel approach to differentiable physics with frictional contacts which represents object shapes implicitly using signed distance fields (SDFs). Our simulation supports contact point calculation even when the involved shapes are nonconvex. Moreover, we propose ways for differentiating the dynamics for the object shape to fa…
Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity in the subsurface. The heterogeneity typically requires high-fidelity physics-based models to make predictions on CO$_2$ fate. Furthermore, characterizing the heterogeneity accurately is fraught with parametric uncertainty. Accounting for both, heterogeneity and uncertainty, makes this a computationally-intensive problem challenging for current reservoir sim…
Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations
Department of Mechanical Engineering（机械工程系）；National University of Singapore（新加坡国立大学）；Institute of High Performance Computing（高性能计算研究所）；Agency for Science, Technology and Research（科学、技术与研究局）；Dept of Mechanical and Aerospace Engineering（机械与航空航天工程系）；Nanyang Technological University（南洋理工大学）
