77 citations · 127 across the 9 of their papers we have counts for
9 papers
Neuro-symbolic partial differential equation solver
Pouria Mistani, Samira Pakravan, Rajesh Ilango +2
We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential equation solvers from existing numerical discretizations found in scientific comp…
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities
Pouria Mistani, Samira Pakravan, Rajesh Ilango +1
We present a scalable strategy for development of mesh-free hybrid neuro-symbolic partial differential equation solvers based on existing mesh-based numerical discretization method…
Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method
Luis Ángel Larios-Cárdenas, Frédéric Gibou
We propose a data-driven mean-curvature solver for the level-set method. This work is the natural extension to of our two-dimensional strategy in [DOI: 10.1007/s1091…
Error-Correcting Neural Networks for Two-Dimensional Curvature Computation in the Level-Set Method
Luis Ángel Larios-Cárdenas, Frédéric Gibou
We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-…
Error-correcting neural networks for semi-Lagrangian advection in the level-set method
Luis Ángel Larios-Cárdenas, Frédéric Gibou
We present a machine learning framework that blends image super-resolution technologies with passive, scalar transport in the level-set method. Here, we investigate whether we can…
A hybrid inference system for improved curvature estimation in the level-set method using machine learning
Luis Ángel Larios-Cárdenas, Frédéric Gibou
We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks…
A fractional stochastic theory for interfacial polarization of cell aggregates
Pouria A. Mistani, Samira Pakravan, Frederic G. Gibou
We present a theoretical framework to model the electric response of cell aggregates. We establish a coarse representation for each cell as a combination of membrane and cytoplasm…
A deep learning approach for the computation of curvature in the level-set method
Luis Ángel Larios-Cárdenas, Frederic Gibou
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neu…
Solving inverse-PDE problems with physics-aware neural networks
Samira Pakravan, Pouria A. Mistani, Miguel Angel Aragon-Calvo +1
We propose a novel composite framework to find unknown fields in the context of inverse problems for partial differential equations (PDEs). We blend the high expressibility of deep…