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A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…

Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…

The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…

Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…

The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a…

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their…

Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

The inability of artificial neural networks to assess the uncertainty of their predictions is an impediment to their widespread use. We distinguish two types of learnable uncertainty: model uncertainty due to a lack of training data and…

We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…

Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are…

This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…

Machine learning methods can be unreliable when deployed in domains that differ from the domains on which they were trained. There are a wide range of proposals for mitigating this problem by learning representations that are ``invariant''…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

This work addresses the inverse identification of apparent elastic properties of random heterogeneous materials using machine learning based on artificial neural networks. The proposed neural network-based identification method requires the…

This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations.…

Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important…

Machine learning techniques have been widely employed as effective tools in addressing various engineering challenges in recent years, particularly for the challenging task of microstructure-informed materials modeling. This work provides a…

Machine learning is revolutionizing chemistry. Beyond the value of predictive models accelerating virtual screening, generative AI aims at enabling inverse design, reversing the compound-to-property prediction paradigm into…