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Found 9 papers, 2 papers with code
FastLRNR and Sparse Physics Informed Backpropagation
We introduce Sparse Physics Informed Backpropagation (SPInProp), a new class of methods for accelerating backpropagation for a specialized neural network architecture called Low Rank Neural Representation (LRNR).
On the performance of sequential Bayesian update for database of diverse tsunami scenarios
The evaluation accuracy of the maximum offshore wave, inundation depth, and its distribution is analyzed to examine the advantages of the scenario superposition method over the previous method.
A Low Rank Neural Representation of Entropy Solutions
We construct a new representation of entropy solutions to nonlinear scalar conservation laws with a smooth convex flux function in a single spatial dimension.
Mining Causality from Continuous-time Dynamics Models: An Application to Tsunami Forecasting
However, parameterization of dynamics using a neural network makes it difficult for humans to identify causal structures in the data.
A range characterization of the single-quadrant ADRT
The range characterization is obtained by first showing that the ADRT is a bijection between images supported on infinite half-strips, then identifying the linear subspaces that stay finitely supported under the inversion formula.
Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems
Classical reduced models are low-rank approximations using a fixed basis designed to achieve dimensionality reduction of large-scale systems.
Exact and fast inversion of the approximate discrete Radon transform from partial data
We give an exact inversion formula for the approximate discrete Radon transform introduced in [Brady, SIAM J.
Model reduction of a parametrized scalar hyperbolic conservation law using displacement interpolation
The key idea of the technique is to construct basis functions that are local in parameter and time space via displacement interpolation.
Numerical Analysis
Imaging of isotropic and anisotropic conductivities from power densities in three dimensions
We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals.
Numerical Analysis Analysis of PDEs 65M32, 35R30, 35J15
