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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Derivative-Informed Neural Operator: An efficient framework for high-dimensional parametric derivative learning
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QuadConv: Quadrature-based convolutions with applications to non-uniform PDE data compression
We present a new convolution layer for deep learning architectures which we call QuadConv — an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. Moreover, the construction of our operator admits an efficient implementation which we detail and construct. As an experimental validation of our operator, we consider the task of compressing partial differential equation (PDE) simulation data from fixed meshes. Here, we show that QuadConv can match the performance of standard discrete convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to a standard convolutional autoencoder (CAE). Further, we show that the QCAE can maintain this accuracy even on non-uniform data. In both cases, QuadConv also outperforms alternative unstructured convolution methods such as graph convolution.
Correcting model misspecification in physics-informed neural networks (PINNs)
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Optimal transport for mesh adaptivity and shock capturing of compressible flows
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Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition
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Full-waveform reconstruction of micro-seismic events via topological derivative approach
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