Partial differential equations meet deep neural networks: A survey
Many problems in science and engineering can be represented by a set of partial differential
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
Multi-Scale Simulation of Complex Systems: A Perspective of Integrating Knowledge and Data
Complex system simulation has been playing an irreplaceable role in understanding,
predicting, and controlling diverse complex systems. In the past few decades, the multi-scale …
predicting, and controlling diverse complex systems. In the past few decades, the multi-scale …
Deep learning of parameterized equations with applications to uncertainty quantification
We propose a learning algorithm for discovering unknown parameterized dynamical
systems by using observational data of the state variables. Our method is built upon and …
systems by using observational data of the state variables. Our method is built upon and …
Microfounded tax revenue forecast model with heterogeneous population and genetic algorithm approach
The ability of governments to accurately forecast tax revenues is essential for the successful
implementation of fiscal programs. However, forecasting state government tax revenues …
implementation of fiscal programs. However, forecasting state government tax revenues …
Fast fitting of neural ordinary differential equations by Bayesian neural gradient matching to infer ecological interactions from time‐series data
W Bonnaffé, T Coulson - Methods in Ecology and Evolution, 2023 - Wiley Online Library
Inferring ecological interactions is hard because we often lack suitable parametric
representations to portray them. Neural ordinary differential equations (NODEs) provide a …
representations to portray them. Neural ordinary differential equations (NODEs) provide a …
MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling
The concept of integrating physics-based and data-driven approaches has become popular
for modeling sustainable energy systems. However, the existing literature mainly focuses on …
for modeling sustainable energy systems. However, the existing literature mainly focuses on …
Entropy structure informed learning for solving inverse problems of differential equations
Y Jiang, W Yang, Y Zhu, L Hong - Chaos, Solitons & Fractals, 2023 - Elsevier
Entropy, since its first discovery by Ludwig Boltzmann in 1877, has been widely applied in
diverse disciplines, including thermodynamics, continuum mechanics, mathematical …
diverse disciplines, including thermodynamics, continuum mechanics, mathematical …
Implementation and (Inverse Modified) Error Analysis for Implicitly Templated ODE-Nets
A Zhu, T Bertalan, B Zhu, Y Tang, IG Kevrekidis - SIAM Journal on Applied …, 2024 - SIAM
We focus on learning unknown dynamics from data using ODE-nets templated on implicit
numerical initial value problem solvers. First, we perform inverse modified error analysis of …
numerical initial value problem solvers. First, we perform inverse modified error analysis of …
PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data
Kinetics of a reaction network that follows mass-action rate laws can be described with a
system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it …
system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it …
Weak collocation regression method: Fast reveal hidden stochastic dynamics from high-dimensional aggregate data
Revealing hidden dynamics from the stochastic data is a challenging problem as the
randomness takes part in the evolution of the data. The problem becomes exceedingly hard …
randomness takes part in the evolution of the data. The problem becomes exceedingly hard …