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Found 6 papers, 3 papers with code
GenFormer: A Deep-Learning-Based Approach for Generating Multivariate Stochastic Processes
Stochastic generators are essential to produce synthetic realizations that preserve target statistical properties.
Operator inference with roll outs for learning reduced models from scarce and low-quality data
Data-driven modeling has become a key building block in computational science and engineering.
Active operator inference for learning low-dimensional dynamical-system models from noisy data
Furthermore, the connection between operator inference and projection-based model reduction enables bounding the mean-squared errors of predictions made with the learned models with respect to traditional reduced models.
Operator inference of non-Markovian terms for learning reduced models from partially observed state trajectories
The core contributions of this work are a data sampling scheme to sample partially observed states from high-dimensional dynamical systems and a formulation of a regression problem to fit the non-Markovian reduced terms to the sampled states.
Probabilistic error estimation for non-intrusive reduced models learned from data of systems governed by linear parabolic partial differential equations
This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control inputs.
Neural network representation of the probability density function of diffusion processes
Numerical examples show that: 1) the neural network solution can approximate the target solution even for partial integro-differential equations and system of PDEs describing the time evolution of the pdf/chf, 2) solving either the Fokker-Planck equation or the chf differential equation using neural networks yields similar pdfs of the state, and 3) the solution to these differential equations can be used to study the behavior of the state for different types of random forcings.
