Thermo-mechanical topology optimization using neural networks with gradient injection

Abstract

Topology optimization using neural networks (TOuNN) parameterizes the density field via a compact fully-connected network and performs design updates through automatic differentiation, ensuring mesh independence and smooth boundaries. Existing TOuNN frameworks are restricted to purely mechanical problems. Under thermo-mechanical coupling, the compliance sensitivity acquires additional contributions from thermal stress and thermal conductivity, which the original loss function cannot capture. This paper proposes a gradient-injected scalar loss that decomposes the total adjoint sensitivity by treating finite-element state quantities (strain energy, temperature, and adjoint temperature) as constants and isolating the differentiable SIMP interpolation functions. During the forward pass, the loss evaluates to the normalized compliance; during backpropagation, its gradient recovers the full three-path adjoint sensitivity. The approach requires neither an end-to-end differentiable finite element solver nor hand-coded backpropagation rules, amounting to a minimal modification of existing TOuNN implementations. Numerical experiments on a half-MBB beam and a cantilever beam demonstrate that the method produces crisp topologies, exhibits robust convergence in the tested cases, and effectively captures the transition from mechanically dominated to thermally dominated behavior.