Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
SIAM, 2011
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The paper introduces a data-informed subspace method with quotient-space Golub-Kahan bidiagonalization and integrated empirical Bayes for efficient posterior approximation in high-dimensional linear inverse problems.
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
Different norm representations of compliance in topology optimization produce distinct structural topologies, with the classical quadratic form yielding well-distributed load paths and the l1-norm form yielding sparse localized members.
citing papers explorer
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Learning Orthonormal Bases for Function Spaces
Neural networks parameterize finite-rank generators for ODEs on the orthogonal Lie group, allowing optimization of orthonormal bases in function space with a universality result that rank-2 generators suffice for density.
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Data-informed posterior approximation for Bayesian linear inverse problems
The paper introduces a data-informed subspace method with quotient-space Golub-Kahan bidiagonalization and integrated empirical Bayes for efficient posterior approximation in high-dimensional linear inverse problems.
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Deep Learning for Subspace Regression
Neural networks regress oversized subspaces for parametric problems using subspace-specific losses, with theory and experiments showing improved accuracy and smoother mappings.
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Comparative Analysis of Compliance-Matrix Induced Norms in Structural Topology Optimization
Different norm representations of compliance in topology optimization produce distinct structural topologies, with the classical quadratic form yielding well-distributed load paths and the l1-norm form yielding sparse localized members.