Probabilistic forecast of nonlinear dynamical systems with uncertainty quantification
arXiv:2305.08942 · doi:10.1016/j.physd.2023.133938
Abstract
Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict new scenarios unobserved before. In this work, we first extend parallel partial Gaussian processes for predicting the vector-valued transition function that links the observations between the current and next time points, and quantify the uncertainty of predictions by posterior sampling. Second, we show the equivalence between the dynamic mode decomposition and the maximum likelihood estimator of the linear mapping matrix in the linear state space model. The connection provides a {probabilistic generative} model of dynamic mode decomposition and thus, uncertainty of predictions can be obtained. Furthermore, we draw close connections between different data-driven models for approximating nonlinear dynamics, through a unified view of generative models. We study two numerical examples, where the inputs of the dynamics are assumed to be known in the first example and the inputs are unknown in the second example. The examples indicate that uncertainty of forecast can be properly quantified, whereas model or input misspecification can degrade the accuracy of uncertainty quantification.
References in corpus (24)
- Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
- Novel type of phase transition in a system of self-driven particles
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS2
- Excitons in atomically thin transition metal dichalcogenides
- A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition
- Observation of giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
- Flocks, herds, and schools: A quantitative theory of flocking
- Optical Spectrum of MoS: Many-body Effects and Diversity of Exciton States
- On Dynamic Mode Decomposition: Theory and Applications
- Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
- BerkeleyGW: A Massively Parallel Computer Package for the Calculation of the Quasiparticle and Optical Properties of Materials and Nanostructures
- Ergodic theory, Dynamic Mode Decomposition and Computation of Spectral Properties of the Koopman operator
- Screening and Many-Body Effects in Two-Dimensional Crystals: Monolayer MoS
- Rates of contraction of posterior distributions based on Gaussian process priors
- A real-time approach to the optical properties of solids and nano-structures: the time-dependent Bethe-Salpeter equation
- First-principles approach to excitons in time-resolved and angle-resolved photoemission spectra
- Learning dynamical systems from data: a simple cross-validation perspective
- The Ensemble Kalman Filter: A Signal Processing Perspective
- Real-time GW: Toward an ab initio description of the ultrafast carrier and exciton dynamics in two-dimensional materials
- Non equilibrium optical properties in semiconductors from first--principles: a combined theoretical and experimental study of bulk silicon
- Reliable emulation of complex functionals by active learning with error control
- Data-driven model construction for anisotropic dynamics of active matter
- Efficient force field and energy emulation through partition of permutationally equivalent atoms