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During the forward pass of Deep Neural Networks (DNNs), inputs gradually transformed from low-level features to high-level conceptual labels. While features at different layers could summarize the important factors of the inputs at varying…
We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model…
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we…
Convergence of Q-learning has been the subject of extensive study for decades. Among the available techniques, the ordinary differential equation (ODE) method is particularly appealing as a general-purpose, off-the-shelf tool for…
This work presents a novel approach for the optimization of dynamic systems on finite-dimensional Lie groups. We rephrase dynamic systems as so-called neural ordinary differential equations (neural ODEs), and formulate the optimization…
We introduce an output layer for neural networks that ensures satisfaction of convex constraints. Our approach, $\Pi$net, leverages operator splitting for rapid and reliable projections in the forward pass, and the implicit function theorem…
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…
Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have…
Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…
In this paper, we consider the problem of synthesizing a controller in the presence of uncertainty such that the resulting closed-loop system satisfies certain hard constraints while optimizing certain (soft) performance objectives. We…
Modeling open quantum dynamics without full knowledge of the system Hamiltonian or noise model is a key challenge in quantum control and quantum state estimation. We introduce an Augmented Quantum Neural Ordinary Differential Equation…
Solving high-dimensional partial differential equations (PDEs) is a major challenge in scientific computing. We develop a new numerical method for solving elliptic-type PDEs by adapting the Q-learning algorithm in reinforcement learning.…
In the realm of high-frequency data streams, achieving real-time learning within varying memory constraints is paramount. This paper presents Ferret, a comprehensive framework designed to enhance online accuracy of Online Continual Learning…
We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…
Obstacle avoidance is central to safe navigation, especially for robots with arbitrary and nonconvex geometries operating in cluttered environments. Existing Control Barrier Function (CBF) approaches often rely on analytic clearance…
Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…
Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…