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.

翻译：瞬态多物理场系统中几何与物理参数的协同优化仍面临挑战，此类系统涉及移动边界、非线性材料响应、相变及多目标冲突。现有方法通常分别优化几何与物理变量，依赖于简化稳态物理模型，或需要离线数据生成与降维设计空间。本文提出一种端到端可微协同优化框架，将几何隐式神经表示与基于JAX编译的欧拉多物理场求解器耦合。几何通过傅里叶特征编码空间坐标的符号距离场表示，边界条件、初始条件、过程控制及材料参数在同一可微循环中优化。连续松弛技术可表征非光滑物理跃迁，同时保持与反向模式自动微分及时间反向传播的兼容性。我们通过瞬态汉堡烹饪基准问题验证该框架——该基准被选作可解释的多物理场问题而非烹饪优化实验。该基准结合了传导与对流传热、潜热效应、水分与脂肪输运、收缩诱导几何演化、动态接触边界条件、翻面诱导的边界条件变化及多目标质量评价。结果表明：仅几何优化通过改变形状缓解热瓶颈，而联合协同优化通过全瞬态推演传播的梯度，将设计响应分散至几何、材料状态、过程变量及边界条件各维度。