Related papers: Machine Learning of Nonlinear Dynamical Systems wi…

Performance of model-based feedforward controllers is typically limited by the accuracy of the inverse system dynamics model. Physics-guided neural networks (PGNN), where a known physical model cooperates in parallel with a neural network,…

Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…

Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables.…

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…

In this paper, we propose a novel neural network structure, namely \emph{feedforward sequential memory networks (FSMN)}, to model long-term dependency in time series without using recurrent feedback. The proposed FSMN is a standard…

This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the…

This work presents an analysis of the effectiveness of using standard shallow feed-forward networks to mimic the behavior of the attention mechanism in the original Transformer model, a state-of-the-art architecture for sequence-to-sequence…

We address a three-tier data-driven approach to solve the inverse problem in complex systems modelling from spatio-temporal data produced by microscopic simulators using machine learning. In the first step, we exploit manifold learning and…

Management and efficient operations in critical infrastructure such as Smart Grids take huge advantage of accurate power load forecasting which, due to its nonlinear nature, remains a challenging task. Recently, deep learning has emerged in…

Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…

We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while…

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments…

In this paper, we introduce the problem of jointly learning feed-forward neural networks across a set of relevant but diverse datasets. Compared to learning a separate network from each dataset in isolation, joint learning enables us to…

Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of…

Differential equations are used in a wide variety of disciplines, describing the complex behavior of the physical world. Analytic solutions to these equations are often difficult to solve for, limiting our current ability to solve complex…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

Feedforward control can greatly improve the response time and control accuracy of any mechatronic system. However, in order to compensate for the effects of modeling errors or disturbances, it is imperative that this type of control works…

As implied by the plethora of literature on graph rewiring, the choice of computational graph employed by a neural network can make a significant impact on its downstream performance. Certain effects related to the computational graph, such…

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition…

We introduce the Fourier Learning Machine (FLM), a neural network (NN) architecture designed to represent a multidimensional nonharmonic Fourier series. The FLM uses a simple feedforward structure with cosine activation functions to learn…