TY - JOUR
T1 - Learning composable energy surrogates for PDE order reduction
AU - Beatson, Alex
AU - Ash, Jordan T.
AU - Roeder, Geoffrey
AU - Xue, Tianju
AU - Adams, Ryan P.
N1 - Funding Information:
Funding: This work was funded by NSF IIS-1421780 and by the Princeton Catalysis Initiative. Other financial interests: RPA is on the board of directors of Cambridge Machines Ltd., and is a scientific advisor to Manifold Bio.
Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.
PY - 2020
Y1 - 2020
N2 - Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour–whether electromagnetic, thermal, or mechanical–arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system’s total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis of individual components. Using dataset aggregation to choose training data allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.
AB - Meta-materials are an important emerging class of engineered materials in which complex macroscopic behaviour–whether electromagnetic, thermal, or mechanical–arises from modular substructure. Simulation and optimization of these materials are computationally challenging, as rich substructures necessitate high-fidelity finite element meshes to solve the governing PDEs. To address this, we leverage parametric modular structure to learn component-level surrogates, enabling cheaper high-fidelity simulation. We use a neural network to model the stored potential energy in a component given boundary conditions. This yields a structured prediction task: macroscopic behavior is determined by the minimizer of the system’s total potential energy, which can be approximated by composing these surrogate models. Composable energy surrogates thus permit simulation in the reduced basis of component boundaries. Costly ground-truth simulation of the full structure is avoided, as training data are generated by performing finite element analysis of individual components. Using dataset aggregation to choose training data allows us to learn energy surrogates which produce accurate macroscopic behavior when composed, accelerating simulation of parametric meta-materials.
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M3 - Conference article
AN - SCOPUS:85102222710
SN - 1049-5258
VL - 2020-December
JO - Advances in Neural Information Processing Systems
JF - Advances in Neural Information Processing Systems
T2 - 34th Conference on Neural Information Processing Systems, NeurIPS 2020
Y2 - 6 December 2020 through 12 December 2020
ER -