Slow invariant manifolds of fast-slow systems of ODEs with physics-informed neural networks
DOI10.1137/24M1656402MaRDI QIDQ6661630
C. I. Siettos, Lucia Russo, Dimitrios G. Patsatzis
Publication date: 13 January 2025
Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)
numerical methodsmachine learningslow invariant manifoldsphysics-informed neural networksfast-slow dynamical systems
Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.) (68T20) Singular perturbations for ordinary differential equations (34E15) Multiple scale methods for ordinary differential equations (34E13) Systems with slow and fast motions for nonlinear problems in mechanics (70K70) Numerical problems in dynamical systems (65P99)
Cites Work
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Title not available (Why is that?)
- Asymptotic analysis of a target-mediated drug disposition model: algorithmic and traditional approaches
- Multiple time scale dynamics
- Semiglobal stabilization of nonlinear systems using fuzzy control and singular perturbation methods
- Enzyme kinetics at high enzyme concentration
- On the validity of the steady state assumption of enzyme kinetics
- Geometric singular perturbation theory for ordinary differential equations
- Truncated Chebyshev series approximation of fuzzy systems for control and nonlinear system identification
- Reduced-space Gaussian process regression for data-driven probabilistic forecast of chaotic dynamical systems
- Equation-free/Galerkin-free POD-assisted computation of incompressible flows
- Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting \textit{in vivo} potency
- Analysis of the computational singular perturbation reduction method for chemical kinetics
- Extending the quasi-steady state approximation by changing variables
- Physics-informed machine learning for reduced-order modeling of nonlinear problems
- A fast and accurate physics-informed neural network reduced order model with shallow masked autoencoder
- An adaptive time-integration scheme for stiff chemistry based on computational singular perturbation and artificial neural networks
- A comparison of neural network architectures for data-driven reduced-order modeling
- Numerical bifurcation analysis of PDEs from lattice Boltzmann model simulations: a parsimonious machine learning approach
- Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
- A new Michaelis-Menten equation valid everywhere multi-scale dynamics prevails
- The total quasi-steady-state approximation for fully competitive enzyme reactions
- Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
- An efficient iterative algorithm for the approximation of the fast and slow dynamics of stiff systems
- Equation-free, coarse-grained multiscale computation: enabling microscopic simulators to perform system-level analysis
- Uncertainty quantification in scientific machine learning: methods, metrics, and comparisons
- Data-driven control of agent-based models: an equation/variable-free machine learning approach
- A User’s View of Solving Stiff Ordinary Differential Equations
- Data-Driven Reduction for a Class of Multiscale Fast-Slow Stochastic Dynamical Systems
- ATTRACTOR MODELING AND EMPIRICAL NONLINEAR MODEL REDUCTION OF DISSIPATIVE DYNAMICAL SYSTEMS
- The partial-equilibrium approximation in reacting flows
- Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
- Model Reduction for Combustion Chemistry
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps
- On Matching, and Even Rectifying, Dynamical Systems through Koopman Operator Eigenfunctions
- The Quasi-Steady-State Assumption: A Case Study in Perturbation
- Quasi steady state and partial equilibrium approximations: their relation and their validity
- DeepXDE: A Deep Learning Library for Solving Differential Equations
- Analysis of the accuracy and convergence of equation-free projection to a slow manifold
- The Koopman Operator in Systems and Control
- SLOW INVARIANT MANIFOLDS AS CURVATURE OF THE FLOW OF DYNAMICAL SYSTEMS
- DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS
- Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes
- Explicit time-scale splitting algorithm for stiff problems: Auto-ignition of gaseous mixtures behind a steady shock
- Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data
- Algorithmic criteria for the validity of quasi-steady state and partial equilibrium models: the Michaelis-Menten reaction mechanism
- Double diffusion maps and their latent harmonics for scientific computations in latent space
- Enabling equation-free modeling via diffusion maps
- Slow invariant manifolds of singularly perturbed systems via physics-informed machine learning
This page was built for publication: Slow invariant manifolds of fast-slow systems of ODEs with physics-informed neural networks
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6661630)