Publication | Open Access
Physics-informed neural networks with hard constraints for inverse design
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2021
Year
Model OptimizationEvolving Neural NetworkEngineeringMachine LearningPhysicsPde-constrained OptimizationPhysic Aware Machine LearningDerivative-free OptimizationLarge Scale OptimizationInverse ProblemsComputer-aided DesignStructural OptimizationDeep LearningInverse DesignPhysics-informed Machine LearningAdjoint MethodsTopology Optimization
Inverse design, especially topology optimization, is widely used across engineering disciplines but is difficult due to high dimensionality and PDE constraints. The authors introduce physics‑informed neural networks with hard constraints (hPINNs) to address topology optimization problems. hPINNs build on standard PINNs by replacing soft constraints with hard constraints via penalty and augmented Lagrangian methods, enabling PDE‑constrained topology optimization without explicit solvers, as demonstrated on holography and Stokes flow examples. hPINNs match conventional adjoint‑based optimization in objective value while producing simpler, smoother designs for non‑unique problems and offering easier implementation.
Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed geometry to achieve targeted properties and the geometry is parameterized by a density function. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method -- physics-informed neural networks with hard constraints (hPINNs) -- for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not rely on any numerical PDE solver. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods.