Related papers: Deep Adversarial Koopman Model for Reaction-Diffus…

Mathematical and computational tools have proven to be reliable in decision-making processes. In recent times, in particular, machine learning-based methods are becoming increasingly popular as advanced support tools. When dealing with…

For a class of reaction cross-diffusion systems of two equations with a cross-diffusion term in the first equation and with self-diffusion terms, we prove that the unique local smooth solution given by Amann theorem is actually global. This…

Imitation learning (IL) enables efficient skill acquisition from demonstrations but often struggles with long-horizon tasks and high-precision control due to compounding errors. Residual policy learning offers a promising, model-agnostic…

Deep Reinforcement Learning (DRL) is a key machine learning technology driving progress across various scientific and engineering fields, including wireless communication. However, its limited interpretability and generalizability remain…

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of…

While language models have made many milestones in text inference and classification tasks, they remain susceptible to adversarial attacks that can lead to unforeseen outcomes. Existing works alleviate this problem by equipping language…

In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…

Despite remarkable achievements in deep learning across various domains, its inherent vulnerability to adversarial examples still remains a critical concern for practical deployment. Adversarial training has emerged as one of the most…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Despite the high performance achieved by deep neural networks on various tasks, extensive studies have demonstrated that small tweaks in the input could fail the model predictions. This issue of deep neural networks has led to a number of…

The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By…

Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current…

This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…

We study the problem of generating adversarial examples in a black-box setting, where we only have access to a zeroth order oracle, providing us with loss function evaluations. Although this setting has been investigated in previous work,…

We propose a novel distributionally robust $Q$-learning algorithm for the non-tabular case accounting for continuous state spaces where the state transition of the underlying Markov decision process is subject to model uncertainty. The…

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)…

The Distributional Koopman Operator (DKO) is introduced as a way to perform Koopman analysis on random dynamical systems where only aggregate distribution data is available, thereby eliminating the need for particle tracking or detailed…

The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach…

The Gray-Scott (GS) model represents the dynamics and steady state pattern formation in reaction-diffusion systems and has been extensively studied in the past. In this paper, we consider the effects of anomalous diffusion on pattern…