arXiv subjects

Adrian S. Wong

Publications and source records attributed to Adrian S. Wong.

5 recordsLinked to original sources

arXiv2025

Contraction and Synchronization in Reservoir Systems

This paper explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing generalized synchronization. Results on continuous time reservoirs make use of the logarithmic norm of the connectivity matrix. Further analysis yields some simple guidelines on how to better construct the connectivity matrix in these systems. Additionally, we outline how the universal approximation property of discrete time reservoirs is readily satisfied by virtue of the activation function being contracting, and how continuous time reservoirs may inherit a limited form of universal approximation due to their overlap with neural ordinary differential equations. The ability of the reservoir computing framework to universally approximate topological conjugates, along with their fast training, make them a compelling data-driven, black-box surrogate of dynamical systems, and a potential candidate for a component of digital twins.

nlin.CD↗

arXiv2022

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).

cs.LG↗

arXiv2021

Robust Forecasting using Predictive Generalized Synchronization in Reservoir Computing

Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting timeseries data. As with all RNNs, selecting the hyperparameters presents a challenge when training onnew inputs. We present a method based on generalized synchronization (GS) that gives direction in designing and evaluating the architecture and hyperparameters of an RC. The 'auxiliary method' for detecting GS provides a computationally efficient pre-training test that guides hyperparameterselection. Furthermore, we provide a metric for RC using the reproduction of the input system's Lyapunov exponentsthat demonstrates robustness in prediction.

physics.comp-ph↗

arXiv2020

Precision annealing Monte Carlo methods for statistical data assimilation and machine learning

In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential equations that describe the dynamics of a physical system. For ML, the model is usually constructed using other strategies. In this paper, we develop a systematic formulation based on Monte Carlo sampling to achieve such information transfer. Following the derivation of an appropriate target distribution, we present the formulation based on the standard Metropolis-Hasting (MH) procedure and the Hamiltonian Monte Carlo (HMC) method for performing the high dimensional integrals that appear. To the extensive literature on MH and HMC, we add (1) an annealing method using a hyperparameter that governs the precision of the model to identify and explore the highest probability regions of phase space dominating those integrals, and (2) a strategy for initializing the state space search. The efficacy of the proposed formulation is demonstrated using a nonlinear dynamical model with chaotic solutions widely used in geophysics.

physics.data-an↗

arXiv2019

Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures

Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods.

stat.CO↗