Related papers: From Initial Data to Boundary Layers: Neural Netwo…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
We study a scalar integro-differential conservation law. The equation was first derived in [2] as the slow erosion limit of granular flow. Considering a set of more general erosion functions, we study the initial boundary value problem for…
Deploying accurate event detection on resource-constrained devices is challenged by the trade-off between performance and computational cost. While Early-Exit (EE) networks offer a solution through adaptive computation, they often fail to…
We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…
Weak stability boundary structures have been widely applied to the analysis on ballistic capture and the construction of low-energy transfers. The first step of this application is to compute/identify weak stability boundary structures.…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate…
We are concerned with hyperbolic systems of order-one linear PDEs originated on non-characteristic manifolds. We put forward a simple but effective method of transforming such initial conditions to standard initial conditions (i.e. when the…
We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…
We consider a hyperbolic conservation law posed on an (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov's method, we derive an L1 error estimate which applies to a…
Neural networks have been very successful in many applications; we often, however, lack a theoretical understanding of what the neural networks are actually learning. This problem emerges when trying to generalise to new data sets. The…
In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…
Humans learn continually throughout their lifespan by accumulating diverse knowledge and fine-tuning it for future tasks. When presented with a similar goal, neural networks suffer from catastrophic forgetting if data distributions across…
The lateral-line system that has evolved in many aquatic animals enables them to navigate murky fluid environments, locate and discriminate obstacles. Here, we present a data-driven model that uses artificial neural networks to process flow…