Related papers: Long-time predictive modeling of nonlinear dynamic…

This paper presents a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network (RNN) models of dynamical systems. A nominal RNN model is first identified using available measurements. The system…

Feed-forward neural networks (FNNs) work as standard building blocks in applying artificial intelligence (AI) to the physical world. They allow learning the dynamics of unknown physical systems (e.g., biological and chemical) {to predict…

Deep neural networks have lately shown tremendous performance in various applications including vision and speech processing tasks. However, alongside their ability to perform these tasks with such high accuracy, it has been shown that they…

Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and…

Unknown nonlinear dynamics often limit the tracking performance of feedforward control. The aim of this paper is to develop a feedforward control framework that can compensate these unknown nonlinear dynamics using universal function…

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize…

Hybrid models and Neural Differential Equations (NDE) are getting increasingly important for the modeling of physical systems, however they often encounter stability and accuracy issues during long-term integration. Training on unrolled…

Data-driven surrogate models can significantly accelerate the simulation of continuous dynamical systems, yet the step-wise accumulation of errors during autoregressive time-stepping often leads to spectral blow-up and unphysical…

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the…

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…

The discovery of linear embedding is the key to the synthesis of linear control techniques for nonlinear systems. In recent years, while Koopman operator theory has become a prominent approach for learning these linear embeddings through…

Machine learning-based weather models have shown great promise in producing accurate forecasts but have struggled when applied to data assimilation tasks, unlike traditional numerical weather prediction (NWP) models. This study introduces…

We describe, implement and test a novel method for training neural networks to estimate the Jacobian matrix $J$ of an unknown multivariate function $F$. The training set is constructed from finitely many pairs $(x,F(x))$ and it contains no…

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…

The regression of a functional response on a set of scalar predictors can be a challenging task, especially if there is a large number of predictors, or the relationship between those predictors and the response is nonlinear. In this work,…

Feedforward neural networks (FNNs) are typically viewed as pure prediction algorithms, and their strong predictive performance has led to their use in many machine-learning applications. However, their flexibility comes with an…

Unknown nonlinear dynamics can limit the performance of model-based feedforward control. The aim of this paper is to develop a feedforward control framework for systems with unknown, typically nonlinear, dynamics. To address the unknown…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

In this paper, we aim at developing scalable neural network-type learning systems. Motivated by the idea of "constructive neural networks" in approximation theory, we focus on "constructing" rather than "training" feed-forward neural…