Differentiable Physics

Simulating rigid-body dynamics with contact in a fast, massively vectorizable, and smoothly differentiable manner is highly desirable in robotics. An important bottleneck faced by existing differentiable simulation frameworks is contact manifold generation: representing the volume of intersection between two colliding geometries via a discrete set of properly distributed contact points. A major factor contributing to this bottleneck is that the related routines of commonly used robotics simulators were not designed with vectorization and differentiability as a primary concern, and thus rely on logic and control flow that hinder these goals. We instead propose a framework designed from the ground up with these goals in mind, by trying to strike a middle ground between: i) convex primitive based approaches used by common robotics simulators (efficient but not differentiable), and ii) mollified vertex-face and edge-edge unsigned distance-based approaches used by barrier methods (differentiable but inefficient). Concretely, we propose: i) a representative set of smooth analytical signed distance primitives to implement vertex-face collisions, and ii) a novel differentiable edge-edge collision routine that can provide signed distances and signed contact normals. The proposed framework is evaluated via a set of didactic experiments and benchmarked against the collision detection routine of the well-established Mujoco XLA framework, where we observe a significant speedup. Supplementary videos can be found at https://github.com/bekeronur/contax, where a reference implementation in JAX will also be made available at the conclusion of the review process.

Estimating simulation-ready scenes from real-world observations is crucial for downstream planning and policy learning tasks. Regretfully, existing methods struggle in cluttered environments, often exhibiting prohibitive computational cost, poor robustness, and restricted generality when scaling to multiple interacting objects. We propose a unified optimization-based formulation for real-to-sim scene estimation that jointly recovers the shapes and poses of multiple rigid objects under physical constraints. Our method is built on two key technical innovations. First, we leverage the recently introduced shape-differentiable contact model, whose global differentiability permits joint optimization over object geometry and pose while modeling inter-object contacts. Second, we exploit the structured sparsity of the augmented Lagrangian Hessian to derive an efficient linear system solver whose computational cost scales favorably with scene complexity. Building on this formulation, we develop an end-to-end Simulation-ready Physics-Aware Reconstruction for Cluttered Scenes (SPARCS) pipeline, which integrates learning-based object initialization, physics-constrained joint shape-pose optimization, and differentiable texture refinement. Experiments on cluttered scenes with up to 5 objects and 22 convex hulls demonstrate that our approach robustly reconstructs physically valid, simulation-ready object shapes and poses. Project webpage: https://rory-weicheng.github.io/SPARCS/.

Exact stochastic simulation of continuous-time Markov chains (CTMCs) is essential when discreteness and noise drive system behavior, but the hard categorical event selection in Gillespie-type algorithms blocks gradient-based learning. We eliminate this constraint by decoupling forward simulation from backward differentiation, with hard categorical sampling generating exact trajectories and gradients propagating through a continuous massively-parallel Gumbel-Softmax straight-through surrogate. Our approach enables accurate optimization at parameter scales over four orders of magnitude beyond existing simulators. We validate for accuracy, scalability, and reliability on a reversible dimerization model (0.09% error), a genetic oscillator (1.2% error), a 203,796-parameter gene regulatory network achieving 98.4% MNIST accuracy (a prototypical deep-learning multilayer perceptron benchmark), and experimental patch-clamp recordings of ion channel gating (R^2 = 0.987) in the single-channel regime. Our GPU implementation delivers 1.9 billion steps per second, matching the scale of non-differentiable simulators. By making exact stochastic simulation massively parallel and autodiff-compatible, our results enable high-dimensional parameter inference and inverse design across systems biology, chemical kinetics, physics, and related CTMC-governed domains.

Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art approaches to this problem either rely on spatial statistics that ignore the governing physics, integrate the physics into a multiple-objective optimization process, or require examples of the complete, fully-resolved simulation state during training, which are frequently unavailable outside of synthetic benchmarks. Here, we present a novel alternative that leverages recent advances in the integration of numerical simulators with data-driven models. Namely, we propose a hybrid modeling pipeline that couples Radial Basis Function (RBF) reconstruction with a Neural Network (NN) correction and a Partial Differential Equation (PDE) solver, so that the numerical simulator itself is embedded directly in the training loop of the learned component. Notably, the NN is trained without assuming availability of examples of the fully-resolved simulation state. This is made possible by implementing the PDE solver so that it is end-to-end differentiable, allowing gradients to be backpropagated through the simulation step during training. This grey-box methodology is evaluated on three standard benchmarks from fluid mechanics, where it achieves superior results over statistical and machine-learning-based reconstruction methods.

Autonomous wire-harness assembly requires precise, reliable manipulation of branched cables, whose deformation is difficult to predict. Models for single Deformable Linear Objects (DLOs) do not extend directly to Branched DLOs (BDLOs), whose junctions couple bending, twisting, and stretching across branches. We introduce Differentiable discrete branched Elastic rods for modeling Furcated DLOs in real-Time (DEFT), a framework combining differentiable physics and learning for accurate BDLO dynamics, real-time inference, and dexterous manipulation planning. DEFT introduces momentum-conserving junction constraints to capture cross-branch coupling, supports mid-structure grasping, uses analytical gradients and branch-parallel computation for efficient parameter learning and inference, and incorporates a residual Graph Neural Network (GNN) to reduce long-horizon prediction errors. Experiments on six physical BDLOs with different topologies and materials demonstrate formulation-level generalization: the same formulation and residual-GNN architecture apply without redesign, with physical and learned parameters fitted separately for each BDLO. DEFT outperforms state-of-the-art physics-based and learning-based methods, achieving RMSEs of 0.93-2.14 cm over five-second recursive open-loop predictions and inference above 100 Hz. In real-world planning, DEFT achieves success rates of 36/40 for shape matching, 40/40 for parent-branch insertion, and 16/20 for child-branch insertion. These results demonstrate accurate, efficient, planning-compatible BDLO prediction for autonomous wire-harness manipulation. Project website: https://roahmlab.github.io/DEFT/.

Robotics simulators have improved significantly in computational speed and scalability, enabling them to generate years of simulated data for complex systems in minutes or hours. Despite these advances, efficiently and accurately computing simulation derivatives remains an open challenge. Addressing this would accelerate the convergence of reinforcement learning and trajectory optimization algorithms, particularly for contact-rich problems. This paper introduces a unifying framework for robotic simulation that accounts for all factors, including dynamics, collisions, and friction. The resulting algorithm computes analytical derivatives of the simulation by implicit differentiation, explicitly handling the intrinsic non-smoothness of the collision and frictional stages while exploiting the sparsity induced by the multi-body structure. Benchmark results demonstrate state-of-the-art performance, with timings ranging from $5\,μ$s for a 7-dof manipulator to $95\,μ$s for a 36-dof humanoid, an improvement of at least two orders of magnitude over alternative methods. Implemented in C++, the code will be open-sourced after the review process to support applications such as simulation-driven learning and real-time control.