Related papers: Unraveling biochemical spatial patterns: machine l…

Machine learning (ML) is emerging as a transformative tool for the design of architected materials, offering properties that far surpass those achievable through lab-based trial-and-error methods. However, a major challenge in current…

A recurrent neural net is described that learns a set of patterns in the presence of noise. The learning rule is of Hebbian type, and, if noise would be absent during the learning process, the resulting final values of the weights would…

Machine learning models have dual-use potential, potentially serving both beneficial and malicious purposes. The development of open-source models in chemistry has specifically surfaced dual-use concerns around toxicological data and…

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement of strand-displacement DNA computing, a large class of…

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…

The problem of morphogenesis and Turing instability are revisited from the point of view of dimensionality effects. First the linear analysis of a generic Turing model is elaborated to the case of multiple stationary states, which may lead…

Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is…

We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward…

We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…

The astounding success of these methods has made it imperative to obtain more explainable and trustworthy estimates from these models. In hydrology, basin characteristics can be noisy or missing, impacting streamflow prediction. For solving…

Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…

We consider a neural network architecture designed to solve inverse problems where the degradation operator is linear and known. This architecture is constructed by unrolling a forward-backward algorithm derived from the minimization of an…

It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…

In a fissile material, the inherent multiplicity of neutrons born through induced fissions leads to correlations in their detection statistics. The correlations between neutrons can be used to trace back some characteristics of the fissile…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy…

The primary issue in inverse halftoning is removing noisy dots on flat areas and restoring image structures (e.g., lines, patterns) on textured areas. Hence, a new structure-aware deep convolutional neural network that incorporates two…

We present a machine learning approach that allows to characterize the disorder potential of a two-dimensional electronic system from its quantum transport properties. Numerically simulated transport data for a large number of disorder…