Related papers: Error analysis based on inverse modified different…
It has long been hoped that model-based control will improve tracking performance while maintaining or increasing compliance. This hope hinges on having or being able to estimate an accurate inverse dynamics model. As a result, substantial…
Uncovering the underlying dynamics from observed data is a critical task in various scientific fields. Recent advances have shown that combining deep learning techniques with linear multistep methods (LMMs) can be highly effective for this…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the…
This article focuses on making discrete-time Adaptive Iterative Learning Control (ILC) more effective using multiple estimation models. Existing strategies use the tracking error to adjust the parametric estimates. Our strategy uses the…
Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. For example, this issue often limits the performance of model-based reinforcement learning and imitation…
Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear…
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…
There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
The integration of discrete algorithmic components in deep learning architectures has numerous applications. Recently, Implicit Maximum Likelihood Estimation (IMLE, Niepert, Minervini, and Franceschi 2021), a class of gradient estimators…
Intelligent diagnosis method based on data-driven and deep learning is an attractive and meaningful field in recent years. However, in practical application scenarios, the imbalance of time-series fault is an urgent problem to be solved.…
Using backward error analysis, we compute implicit training biases in multitask and continual learning settings for neural networks trained with stochastic gradient descent. In particular, we derive modified losses that are implicitly…
A modified Deep BSDE (backward differential equation) learning method with measurability loss, called Deep BSDE-ML method, is introduced in this paper to solve a kind of linear decoupled forward-backward stochastic differential equations…
Hybrid dynamical systems are prevalent in science and engineering to express complex systems with continuous and discrete states. To learn the laws of systems, all previous methods for equation discovery in hybrid systems follow a two-stage…
In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…