[HTML][HTML] Fully probabilistic deep models for forward and inverse problems in parametric PDEs
We introduce a physics-driven deep latent variable model (PDDLVM) to learn
simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of …
simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of …
Generating synthetic data for neural operators
Numerous developments in the recent literature show the promising potential of deep
learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the …
learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the …
Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media
M Chatzopoulos, PS Koutsourelakis - arXiv preprint arXiv:2405.19019, 2024 - arxiv.org
We propose Physics-Aware Neural Implicit Solvers (PANIS), a novel, data-driven framework
for learning surrogates for parametrized Partial Differential Equations (PDEs). It consists of a …
for learning surrogates for parametrized Partial Differential Equations (PDEs). It consists of a …
Efficient Prior Calibration From Indirect Data
Bayesian inversion is central to the quantification of uncertainty within problems arising from
numerous applications in science and engineering. To formulate the approach, four …
numerous applications in science and engineering. To formulate the approach, four …
Φ-DVAE: Physics-Informed Dynamical Variational Autoencoders for Unstructured Data Assimilation
Incorporating unstructured data into physical models is a challenging problem that is
emerging in data assimilation. Traditional approaches focus on well-defined observation …
emerging in data assimilation. Traditional approaches focus on well-defined observation …
Ensemble models outperform single model uncertainties and predictions for operator-learning of hypersonic flows
High-fidelity computational simulations and physical experiments of hypersonic flows are
resource intensive. Training scientific machine learning (SciML) models on limited high …
resource intensive. Training scientific machine learning (SciML) models on limited high …
Learning from the Future: Improve Long-term Mesh-based Simulation with Foresight
This paper studies the problem of learning mesh-based physical simulations, a crucial task
with applications in fluid mechanics and aerodynamics. Recent works typically utilize graph …
with applications in fluid mechanics and aerodynamics. Recent works typically utilize graph …