Related papers: Machine Learning Accelerated PDE Backstepping Obse…

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled…

Deep neural networks that approximate nonlinear function-to-function mappings, i.e., operators, which are called DeepONet, have been demonstrated in recent articles to be capable of encoding entire PDE control methodologies, such as…

This paper develops an adaptive observation-based efficient reinforcement learning (RL) approach for systems with uncertain drift dynamics. A novel concurrent learning adaptive extended observer (CL-AEO) is first designed to jointly…

This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…

State estimation is an important aspect in many robotics applications. In this work, we consider the task of obtaining accurate state estimates for robotic systems by enhancing the dynamics model used in state estimation algorithms.…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

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…

This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be…

Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian -- the evolution of the trained system only depends on the current…

We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a…

We develop a non-collocated, observer-based output-feedback law for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of $n+m$, general heterodirectional hyperbolic systems as $n\to\infty$. The…

Flood inundation forecast provides critical information for emergency planning before and during flood events. Real time flood inundation forecast tools are still lacking. High-resolution hydrodynamic modeling has become more accessible in…

We present a novel methodology for designing output-feedback backstepping boundary controllers for an unstable 1-D diffusion-reaction partial differential equation with spatially-varying reaction. Using "folding" transforms the parabolic…

The problem of effective use of Phasor Measurement Units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use this new measurements to reconstruct the state of the…

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…

Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…