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The forward problems of pattern formation have been greatly empowered by extensive theoretical studies and simulations, however, the inverse problem is less well understood. It remains unclear how accurately one can use images of pattern…
Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict…
Accurate and robust spatial orders are ubiquitous in living systems. In 1952, Alan Turing proposed an elegant mechanism for pattern formation based on spontaneous breaking of the spatial translational symmetry in the underlying…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio-temporal pattern can be generated by a genetic network involving a sufficiently large number of genes.…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
Turing patterns are fundamental in biophysics, emerging from short-range activation and long-range inhibition processes. However, their paradigm is based on diffusive transport processes, which yields Turing patters that are less sharp than…
We review a recent trend in computational systems biology which aims at using pattern recognition algorithms to infer the structure of large-scale biological networks from heterogeneous genomic data. We present several strategies that have…
Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
Data inconsistency leads to a slow training process when deep neural networks are used for the inverse design of photonic devices, an issue that arises from the fundamental property of non-uniqueness in all inverse scattering problems. Here…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Turing presented a general representation scheme by which to achieve artificial intelligence - unorganised machines. Significantly, these were a form of discrete dynamical system and yet such representations remain relatively unexplored.…
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…
Learning-based methods have demonstrated remarkable performance in solving inverse problems, particularly in image reconstruction tasks. Despite their success, these approaches often lack theoretical guarantees, which are crucial in…
This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with…
The design of metamaterials which support unique optical responses is the basis for most thin-film nanophotonics applications. In practice this inverse design problem can be difficult to solve systematically due to the large design…
This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…