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Found 7 papers, 7 papers with code
Learning Constitutive Relations using Symmetric Positive Definite Neural Networks
We present the Cholesky-factored symmetric positive definite neural network (SPD-NN) for modeling constitutive relations in dynamical equations.
Numerical Analysis Numerical Analysis
Physics Constrained Learning for Data-driven Inverse Modeling from Sparse Observations
Our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.
Numerical Analysis Numerical Analysis
Learning Hidden Dynamics using Intelligent Automatic Differentiation
Numerical tests demonstrate the feasibility of IAD for learning hidden dynamics in complicated systems of PDEs; additionally, by incorporating custom built state adjoint method codes in IAD, we significantly accelerate the forward and inverse simulation.
Numerical Analysis Numerical Analysis
Time-lapse Full Waveform Inversion for Subsurface Flow Problems with Intelligent Automatic Differentiation
We describe a novel framework for PDE (partial-differential-equation)-constrained full-waveform inversion (FWI) that estimates parameters of subsurface flow processes, such as rock permeability and porosity, using time-lapse observed data.
Geophysics
Adversarial Numerical Analysis for Inverse Problems
Many scientific and engineering applications are formulated as inverse problems associated with stochastic models.
Numerical Analysis Numerical Analysis
Predictive Modeling with Learned Constitutive Relations from Indirect Observations
Its counterparts, like piecewise linear functions and radial basis functions, are compared, and the strength of neural networks is explored.
Numerical Analysis Numerical Analysis Computational Physics
Calibrating Multivariate Lévy Processes with Neural Networks
Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and results to date are mostly in 1D.
