Search Results for author:
Found 14 papers, 4 papers with code
Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems
Uncertainty in the inverse solution is quantified in terms of the posterior distribution of CKLE coefficients, and we sample the posterior by solving a randomized PICKLE minimization problem, formulated by adding zero-mean Gaussian perturbations in the PICKLE loss function.
Physics-informed machine learning
Uncertainty Quantification
Conditional Korhunen-Loéve regression model with Basis Adaptation for high-dimensional problems: uncertainty quantification and inverse modeling
We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems as a function of the systems' spatially heterogeneous parameter fields with applications to uncertainty quantification and parameter estimation in high-dimensional problems.
Gaussian process regression and conditional Karhunen-Loéve models for data assimilation in inverse problems
On the other hand, in CKLEMAP, the number of unknowns (CKLE coefficients) is controlled by the smoothness of the parameter field and the number of measurements, and is in general much smaller than the number of discretization nodes, which leads to a significant reduction of computational cost with respect to the standard MAP method.
Physics-Informed Neural Network Method for Parabolic Differential Equations with Sharply Perturbed Initial Conditions
We propose a normalized form of ADE where the initial perturbation of the solution does not decrease in amplitude and demonstrate that this normalization significantly reduces the PINN approximation error.
Physics-Informed Machine Learning Method for Large-Scale Data Assimilation Problems
In our approach, we extend the physics-informed conditional Karhunen-Lo\'{e}ve expansion (PICKLE) method for modeling subsurface flow with unknown flux (Neumann) and varying head (Dirichlet) boundary conditions.
BIG-bench Machine Learning
Physics-informed machine learning
Physics-informed CoKriging model of a redox flow battery
Redox flow batteries (RFBs) offer the capability to store large amounts of energy cheaply and efficiently, however, there is a need for fast and accurate models of the charge-discharge curve of a RFB to potentially improve the battery capacity and performance.
Physics-Informed Gaussian Process Regression for Probabilistic States Estimation and Forecasting in Power Grids
For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR, with both forecasts being significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast.
Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems
Time series forecasting remains a central challenge problem in almost all scientific disciplines.
Learning Unknown Physics of non-Newtonian Fluids
Once a viscosity model is learned, we use the PINN method to solve the momentum conservation equation for non-Newtonian fluid flow using only the boundary conditions.
Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport
We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for joint inversion of the conductivity, hydraulic head, and concentration fields in a steady-state advection--dispersion problem.
Electric Load and Power Forecasting Using Ensemble Gaussian Process Regression
We propose a new forecasting method for predicting load demand and generation scheduling.
Learning Parameters and Constitutive Relationships with Physics Informed Deep Neural Networks
We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation.
Analysis of PDEs Computational Physics
Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks
We suggest ways to enforce given constraints in the output of a Generative Adversarial Network (GAN) generator both for interpolation and extrapolation (prediction).
Solving differential equations with unknown constitutive relations as recurrent neural networks
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term.
