# Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark

arXiv: https://arxiv.org/abs/2605.01040 · HTML: https://mlsanity.com/paper/2605.01040/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 9 of 9)

- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science](https://mlsanity.com/paper/2212.00964/) (2022)
- [A Review of Differentiable Simulators](https://mlsanity.com/paper/2407.05560/) (2024)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [MORPH: Design Co-optimization with Reinforcement Learning via a Differentiable Hardware Model Proxy](https://mlsanity.com/paper/2309.17227/) (2023)
- [Surrogate-Based Optimization Techniques for Process Systems Engineering](https://mlsanity.com/paper/2412.13948/) (2024)

## Abstract (arXiv)

The co-optimization of geometry and physical parameters remains challenging in transient multiphysics systems involving moving boundaries, nonlinear material response, phase transitions, and competing objectives. Existing methods often optimize geometry and physical variables separately, rely on simplified steady-state physics, or require offline data generation and reduced design spaces. Here, we present an end-to-end differentiable co-optimization framework that couples an implicit neural representation of geometry with a JAX-compiled Eulerian multiphysics solver. Geometry is represented as a signed distance field using Fourier-feature-encoded spatial coordinates, while boundary conditions, initial conditions, process controls, and material parameters are optimized within the same differentiable loop. Continuous relaxations represent non-smooth physical transitions while preserving compatibility with reverse-mode automatic differentiation and backpropagation through time. We demonstrate the framework using a transient hamburger-cooking benchmark, selected as an interpretable multiphysics problem rather than a culinary optimization exercise. The benchmark combines conductive and convective heat transfer, latent energy effects, moisture and fat transport, shrinkage-induced geometry evolution, evolving contact boundary conditions, flipping-induced boundary-condition changes, and competing quality objectives. Results show that geometry-only optimization modifies shape to relieve thermal bottlenecks, while joint co-optimization distributes the design response across geometry, material state, process variables, and boundary conditions through gradients propagated over the full transient rollout.