differentiable physics optimization

In engineering design, the non-differentiability of conventional CAE workflows—particularly mesh generation and physics simulation—hinders gradient-based high-dimensional optimization. To address this, we propose an end-to-end differentiable shape optimization framework: geometry is represented via signed distance fields (SDFs), and a 3D U-Net serves as a full-field surrogate model that directly learns the mapping from SDFs to physical fields (e.g., pressure, velocity), thereby bypassing non-differentiable components without requiring differentiable solvers or adjoint methods. The surrogate is embedded within a differentiable optimization pipeline, enabling backpropagation to compute gradients with respect to design parameters. Evaluated on aerodynamic shape optimization, our method achieves fully gradient-driven, efficient iterative design refinement. Results demonstrate substantial improvements in optimization efficiency and validate the framework’s feasibility and advantages in complex engineering applications.

Existing differentiable optimization frameworks suffer from fragmented modeling interfaces, cumbersome parameter differentiation, and poor solver compatibility. This paper introduces the first general-purpose, differentiable optimization framework natively supporting parametric JuMP modeling. Grounded in the Karush–Kuhn–Tucker (KKT) conditions and under standard regularity assumptions, it unifies forward- and reverse-mode sensitivity analysis for both convex and nonconvex problems. Key contributions include: (1) first-class parameter abstractions enabling automatic, named-parameter differentiation across objectives and constraints—eliminating low-level coefficient manipulation; (2) deep integration with DiffOpt.jl and the JuMP ecosystem while preserving solver agnosticism; and (3) empirical validation on economic dispatch, portfolio optimization, and robotic inverse kinematics, plus successful deployment in energy market bidding and end-to-end Sobolev training—demonstrating substantial improvements in the modeling–optimization–learning feedback loop efficiency.

In scientific computing applications—such as trajectory prediction, optimal control, and minimum energy path computation—downstream algorithms critically depend on accurate model evaluations. Conventional mean-squared-error-based supervised learning often induces task-specific performance degradation due to misalignment between the loss function and the ultimate algorithmic objective. Method: We propose a task-oriented predictive modeling paradigm that replaces standard regression losses with a surrogate objective: the maximum prediction error over a downstream task support set. Our framework integrates sampling measure modeling, empirical risk discretization, and iterative optimization to directly optimize downstream algorithmic performance. Contribution/Results: This is the first approach to explicitly embed downstream robustness requirements into the training objective. Evaluated across multiple scientific computing benchmarks, it consistently improves both predictive accuracy and algorithmic stability, demonstrating superior generalization under task-relevant perturbations.

This work addresses the low policy-generation efficiency and objective mismatch prevalent in model-based reinforcement learning (MBRL) and imitation learning. We propose a unified framework wherein policies are represented via differentiable trajectory optimization. Methodologically, we jointly learn the cost function and dynamics model end-to-end, optimizing model parameters directly through backpropagation of policy-gradient losses—enabling task-performance-driven learning. Notably, this is the first MBRL approach to explicitly resolve the “objective mismatch” problem. To enhance policy robustness, we innovatively integrate energy-based models with diffusion models to construct a contrastive learning mechanism. Extensive evaluation across 15 MBRL benchmark tasks and 35 high-dimensional visual/point-cloud imitation learning tasks demonstrates consistent superiority over state-of-the-art methods, validating the framework’s effectiveness and broad generalizability.

Existing physics engines for robotics struggle to simultaneously ensure stable simulation, high-fidelity rigid contact modeling, and full differentiability with respect to states, actions, and system parameters. To address this, we propose Dojo—the first end-to-end differentiable physics engine designed specifically for robotics. Dojo uniquely integrates variational integrators with a second-order cone nonlinear complementarity problem (NCP) solver, guaranteeing energy and momentum conservation during contact and enabling smooth, analytic gradient computation across contact events. It further employs a customized primal-dual interior-point method for efficient implicit differentiation. Evaluated on motion planning, policy optimization, and system identification tasks, Dojo demonstrates significantly improved gradient accuracy and faster optimization convergence in challenging rigid-contact scenarios.

This work addresses the low sample efficiency of traditional model-free reinforcement learning methods—such as Proximal Policy Optimization (PPO)—which rely on high-variance advantage estimates. The authors propose Analytic Policy Gradients (APG), a method that leverages differentiable environment dynamics to compute exact, end-to-end gradients of policy returns with respect to policy parameters. To mitigate gradient degradation in long-horizon tasks, APG incorporates a segment-wise backpropagation mechanism and combines Monte Carlo estimation with critic-guided bootstrapping for effective gradient guidance. Evaluated on four continuous control benchmarks under identical network architectures and training protocols, APG consistently outperforms PPO, demonstrating substantially higher sample efficiency and faster convergence.

Providing efficient and differentiable reachability guarantees for neural network-controlled closed-loop systems under uncertainty remains a significant challenge. This work proposes the first parallelized reachability analysis framework that supports GPU batch processing and automatic differentiation, integrating Taylor model flowpipes with CROWN-style linear bound propagation to enable differentiable computation while preserving affine dependencies. By bridging the gap between formal verification and learning-based planning, the method facilitates reachability-aware sampling-based model predictive control (MPC). Evaluated on non-prehensile manipulation and quadrotor tasks, the approach enables online planning for systems up to 72 dimensions, delivering precise reachability certificates under bounded uncertainty while maintaining real-time performance.

Existing differentiable PDE solvers lack a unified benchmark to evaluate their practical performance in terms of gradient correctness, computational overhead, numerical stability, and ease of integration. This work proposes an extensible benchmarking framework that, through containerized encapsulation (Tesseract) and a standardized gradient API, supports cross-language interoperability and multiple automatic differentiation strategies. For the first time, it enables a systematic comparison of 14 differentiable solvers spanning fluid dynamics, structural mechanics, and heat transfer. Experiments reveal order-of-magnitude differences in computational cost and Jacobian condition numbers across solvers, yet all converge to similar optimal solutions. These findings indicate that real-world bottlenecks lie primarily in memory consumption, numerical stability, and compatibility—not in optimization capability.