# Differentiable solver for time-dependent deformation problems with contact

arXiv: https://arxiv.org/abs/2205.13643 · HTML: https://mlsanity.com/paper/2205.13643/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2022.

## Built on by (most cited first, 12 of 12)

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- [TopoGaussian: Inferring Internal Topology Structures from Visual Clues](https://mlsanity.com/paper/2503.12343/) (2025)
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- [Differentiate the Solver, Not the Equation: Reverse-Sweep Adjoints for Block Implicit Simulation](https://mlsanity.com/paper/2608.08559/) (2026)
- [Rigid Body Adversarial Attacks](https://mlsanity.com/paper/2502.05669/) (2025)
- [Iskra: A System for Inverse Geometry Processing](https://mlsanity.com/paper/2602.12105/) (2026)
- [GaussiAnimate: Rig Animatable Categories with Level of Dynamics](https://mlsanity.com/paper/2604.08547/) (2026)
- [An Efficient Multilevel Preconditioned Nonlinear Conjugate Gradient Method for Incremental Potential Contact](https://mlsanity.com/paper/2604.19892/) (2026)
- [RealSimLoop: Online Real-to-Sim Adaptation via Differentiable Reduced-Order Simulation with Vision Feedback](https://mlsanity.com/paper/2609.09828/) (2026)

## Abstract (arXiv)

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry. It supports static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.