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Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more…

By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…

We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…

A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously…

In this paper we present a simulation study of water-like anomalies in core-softened system introduced in our previous publications. We investigate the anomalous regions for a system with the same functional form of the potential but with…

Accurately determining the crystallographic structure of a material, organic or inorganic, is a critical primary step in material development and analysis. The most common practices involve analysis of diffraction patterns produced in…

Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…

Spontaneous structural relaxation is intrinsic to glassy materials due to their metastable nature. For phase-change materials (PCMs), the resultant temporal change in electrical resistance seriously hamper in-memory computing (IMC)…

This paper aims to solve numerically the two-dimensional inverse medium scattering problem with far-field data. This is a challenging task due to the severe ill-posedness and strong nonlinearity of the inverse problem. As already known, it…

Theoretical simulation to phase change materials such as Ge-Sb-Te has suffered from two methodology issues. On the one hand, there is a lack of efficient band gap correction method for density functional theory, which is suitable for these…

Materials discovery is fundamental to advance next-generation technologies as well as for sustainable and circular economy. Beyond computational screening, generative models are efficient at finding materials with desired properties, via…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…

The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in…

The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions…

Designing free-form photonic devices is fundamentally challenging due to the vast number of possible geometries and the complex requirements of fabrication constraints. Traditional inverse-design approaches--whether driven by human…

By using molecular dynamics simulation, formation mechanisms of amorphous carbon in particular sp${}^3$ rich structure was researched. The problem that reactive empirical bond order potential cannot represent amorphous carbon properly was…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

The use of machine learning is becoming increasingly common in computational materials science. To build effective models of the chemistry of materials, useful machine-based representations of atoms and their compounds are required. We…

Due to the high potential for abuse of GenAI systems, the task of detecting synthetic images has recently become of great interest to the research community. Unfortunately, existing image-space detectors quickly become obsolete as new…