Related papers: Neural Operators for Adaptive Control of Traffic F…
Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional…
Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
We present a method to solve initial and boundary value problems using artificial neural networks. A trial solution of the differential equation is written as a sum of two parts. The first part satisfies the boundary (or initial) conditions…
In this paper, a novel adaptive tuning method of PID neural network (PIDNN) controller for nonlinear process is proposed. The method utilizes an improved gradient descent method to adjust PIDNN parameters where the margin stability will be…
The deployment of Autonomous Vehicles (AVs) poses considerable challenges and unique opportunities for the design and management of future urban road infrastructure. In light of this disruptive transformation, the Right-Of-Way (ROW)…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…
We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…
Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
Learning-based autonomous driving requires continuous integration of diverse knowledge in complex traffic , yet existing methods exhibit significant limitations in adaptive capabilities. Addressing this gap demands autonomous driving…
Driverless vehicles are complex systems operating in constantly changing environments. Automated driving is achieved by controlling the coupled longitudinal and lateral vehicle dynamics. Model predictive control is one of the most promising…
Partial differential equations often contain unknown functions that are difficult or impossible to measure directly, hampering our ability to derive predictions from the model. Workflows for recovering scalar PDE parameters from data are…
Road condition is an important environmental factor for autonomous vehicle control. A dramatic change in the road condition from the nominal status is a source of uncertainty that can lead to a system failure. Once the vehicle encounters an…
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…
Modeling complex spatial and temporal correlations in the correlated time series data is indispensable for understanding the traffic dynamics and predicting the future status of an evolving traffic system. Recent works focus on designing…
A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…