Related papers: Gain-Only Neural Operators for PDE Backstepping

This paper introduces Selective-Backprop, a technique that accelerates the training of deep neural networks (DNNs) by prioritizing examples with high loss at each iteration. Selective-Backprop uses the output of a training example's forward…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

Neural PDE simulators often receive only a single observed field at deployment. In this setting, a field-to-future predictor can collapse distinct latent problem states into the same deterministic interface, losing the ambiguity needed for…

Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this paper, we tailor the…

Machine learning models are often learned by minimising a loss function on the training data using a gradient descent algorithm. These models often suffer from overfitting, leading to a decline in predictive performance on unseen data. A…

Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations the message passing…

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…

Composite adaptive radial basis function neural network (RBFNN) control with a lattice distribution of hidden nodes has three inherent demerits: 1) the approximation domain of adaptive RBFNNs is difficult to be determined a priori; 2) only…

We consider a nonlinear control system modeled as an ordinary differential equation subject to disturbance, with a state feedback controller parameterized as a feedforward neural network. We propose a framework for training controllers with…

Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability…

We present a new a priori analysis of a class of collocation methods for parabolic PDEs that rely only on pointwise data of force term, boundary data, and initial data. Under Besov regularity assumptions, we characterize the optimal…

Despite recent advances in Graph Neural Networks (GNNs), their training strategies remain largely under-explored. The conventional training strategy learns over all nodes in the original graph(s) equally, which can be sub-optimal as certain…

Despite the numerous advances, reinforcement learning remains away from widespread acceptance for autonomous controller design as compared to classical methods due to lack of ability to effectively tackle the reality gap. The reliance on…

Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified…

In this paper, we present a Stochastic Deep Neural Network-based Model Reference Adaptive Control. Building on our work "Deep Model Reference Adaptive Control", we extend the controller capability by using Bayesian deep neural networks…

Adversarial Training (AT) with Projected Gradient Descent (PGD) is an effective approach for improving the robustness of the deep neural networks. However, PGD AT has been shown to suffer from two main limitations: i) high computational…

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state…

Scientific computing using deep learning has seen significant advancements in recent years. There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding…