Differential equation-constrained optimization with stochasticity

DOI10.1137/23m1571162zbMATH Open1540.49041MaRDI QIDQ6554975

Qin Li, Li Wang, Yunan Yang

Publication date: 13 June 2024

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

zbMATH Keywords

inverse problemconstrained optimizationparticle methodWasserstein gradient flowpush-forward map

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Inverse problems in optimal control (49N45) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75) Optimal transportation (49Q22)

Cites Work

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• Stochastic spectral methods for efficient Bayesian solution of inverse problems
• A convexity principle for interacting gases
• A blob method for diffusion
• Mirror descent and nonlinear projected subgradient methods for convex optimization.
• Hessian informed mirror descent
• The Bayesian update: variational formulations and gradient flows
• Kinetic methods for inverse problems
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Density estimation
• Data assimilation -- mathematical foundation and applications. Abstracts from the workshop held February 20--26, 2022
• Inverse problems: A Bayesian perspective
• The Variational Formulation of the Fokker--Planck Equation
• Ensemble Markov Chain Monte Carlo with Teleporting Walkers
• Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman Sampler
• Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems

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