Defesa de Dissertação de Mestrado: Deep Operator Networks as Differentiable Surrogate Models in Bayesian Calibration Problems

Orientadores:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC
Marcio Rentes Borges - Laboratório Nacional de Computação Científica - LNCC
José Luiz Faccini

Banca Examinadora:
Gilson Antônio Giraldi - Laboratório Nacional de Computação Científica - LNCC (presidente)
Renato Simões Silva - Laboratório Nacional de Computação Científica - LNCC
Helcio Rangel Barreto Orlande - UFRJ - Departamento/Programa de Engenharia Mecânica - UFRJ/COPPE

Suplentes:
Regina Célia Cerqueira de Almeida - Laboratório Nacional de Computação Científica - LNCC
Alan Miranda Monteiro de Lima - Universidade Federal do Rio de Janeiro - UFRJ

Resumo:

The computation al expense of gradient evaluations remains a primary bottleneck for the widespread adoption of Hamiltonian Monte Carlo (HMC) in large-scale, high-dimensional Bayesian inverse problems. This work addresses this challenge by employing Deep Operator Networks (DeepONets) as fast, differentiable surrogate models. By learning nonlinear operators from data, DeepONets provide accurate approximations of complex system dynamics while preserving the gradient information essential for efficient HMC sampling via automatic differentiation. We experimentally validate that the gradiente structure of the original simulator is effectively preserved within the DeepONet-surrogate framework, enabling the immediate convergence of HMC. This is demonstrated on two canonical problems: a lightweight damped pendulum inversion, used for nuanced methodological exploration, and a high-dimensional stationary groundwater flow problem for inferring permeability fields. Our approach yields substantial computational gains: for the pendulum problem, we observe a 150x speedup in likelihood evaluations and a 50x speedup in gradient evaluations compared to the original simulator with finite-difference gradients. For the groundwater problem, we achieve over 700x and 7,000x speedups in evaluation and gradient computation, respectively. Fast convergence is confirmed with HMC contrasting with the thousands of steps required by a standard Markov Chain Monte Carlo (MCMC) method.