Peter M. Dower

Viv Bone, Chris van der Heide, Kieran Mackle et al.

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modelling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, especially when they are generated by computational models that are compatible with automatic differentiation or have adjoint solutions. Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and a realistic partial differential equation problem, where we predict the aerodynamic coefficients of a hypersonic flight vehicle over a range of flight conditions and geometries. In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.

Yuansan Liu, Jeygopi Panisilvam, Peter Dower et al.

Deep Learning has been a critical part of designing inverse design methods that are computationally efficient and accurate. An example of this is the design of photonic metasurfaces by using their photoluminescent spectrum as the input data to predict their topology. One fundamental challenge of these systems is their ability to represent nonlinear relationships between sets of data that have different dimensionalities. Existing design methods often implement a conditional Generative Adversarial Network in order to solve this problem, but in many cases the solution is unable to generate structures that provide multiple peaks when validated. It is demonstrated that in response to the target spectrum, the Bidirectional Adversarial Autoencoder is able to generate structures that provide multiple peaks on several occasions. As a result the proposed model represents an important advance towards the generation of nonlinear photonic metasurfaces that can be used in advanced metasurface design.

Jérôme Darbon, Peter M. Dower, Tingwei Meng

Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are respectively used to compute the value function and the optimal control for certain class of high dimensional optimal control problems. We provide the mathematical analysis for the two abstract architectures. We also show several numerical results computed using the deep neural network implementations of these abstract architectures. A preliminary implementation of our proposed neural network architecture on FPGAs shows promising speed up compared to CPUs. This work paves the way to leverage efficient dedicated hardware designed for neural networks to solve high dimensional optimal control problems and Hamilton-Jacobi PDEs.