Open Postdoc position

Metamaterials designed by AI for Sustainable Steel

Staff: Corentin Coulais (, Jan-Willem van de Meent (
Institutes: Institute of Physics, Institute of Informatics

To apply: reach out to Me and Jan-Willem and apply via this link.

In this project, we will develop deep learning methods to accelerate the computational design of dissipative metamaterials that will in turn enable new technology for sustainable steel.

Computational design of metamaterials will require solving fundamental research problems at the intersection of materials science and AI research. The response of steel metamaterials is highly nonlinear, as it involves a mechanical instability called buckling, irreversible plastic deformations and self-contact interactions. Previous work by Coulais demonstrated that convolutional neural networks are extremely efficient at classifying metamaterials and can be combined with genetic algorithms to find materials with optimal properties. This project will build on this line of work, which was carried out in the static linear regime, to reason about dynamic nonlinear responses.

WP1: Learning a coarse-grained model from finite-element simulations. The technical challenge in modeling the dissipative dynamics of metamaterials is that numerical simulation with traditional finite-element methods is prohibitively expensive, even for a single configuration. To address this challenge, we will begin by developing AI methods that approximate dynamics at the level of a unit cell. The input to the model will be a large collection of small-scale finite-element simulations, which can be generated relatively cheaply. To account for memory-effects in the material, we will train a neural sequence model, such as a recurrent neural network, to predict the pairwise forces between the elements of the coarse-grained model in a matter that mirror the finite-element dynamics.

WP2: Learning a surrogate function for the coarse-grained dynamics. A coarse-grained model will reduce O(50k) finite elements into O(10) coarse-grained particles per unit cell. This will make it possible to simulate dissipative dynamics for multiple configurations. However, it will still not be feasible to test all configurations that need to be considered during optimization. To screen candidate configurations, we will train a fast surrogate model to predict macroscopic response variables from coarse-grained simulations. This model will take the form of a graph neural network that is equivariant, viz. where translations and rotations of inputs are baked into the networks. These equivariant architectures, which have in part been pioneered at AMLab, will allow us to train a surrogate model from a comparatively small number of coarse-grained simulations by generalizing across inputs that are equivalent up to rotations and translations.

WP3: Bayesian combinatorial optimization of meta-material configurations. Our ultimate goal is to define an outer optimization loop that maximizes shock-damping performance subject to a carbon footprint budget, or conversely minimizes the carbon footprint budget subject to damping performance requirements. This involves repeatedly running coarse-grained simulations in a manner that balances exploration (testing new configurations with uncertain properties) and exploitation (improving on the current best candidate). To this end, we will employ the learned surrogate model to compute similarities between unseen candidate configurations and previously simulated configurations. The resulting Bayesian optimization procedure should allow us to identify an optimum based on O(100) simulations.

Expected outcomes and Impact: Metamaterials are currently at an early technology readiness level, so this project carries risks that are inherent to all fundamental research. However solving these fundamental challenges can substantially contribute to the greenification by (i) improving vehicle efficiency through the development of stronger and lighter metamaterials that meet the energy-adsorption requirements for aerospace and automotive applications, (ii) enabling construction of parts that employ lower-grade steel as the base material, which takes less CO2 to produce than high-grade steels and other metals.

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