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A fundamental challenge in the design of photonic devices, and electromagnetic structures more generally, is the optimization of their overall architecture to achieve a desired response. To this end, topology or shape optimizers based on…

Numerical data structures for positive dimensional solution sets of polynomial systems are sets of generic points cut out by random planes of complimentary dimension. We may represent the linear spaces defined by those planes either by…

Titanium is the base material for a number of technologically important alloys for energy conversion and structural applications. Atomic-scale studies of Ti-based metals employing first-principles methods, such as density functional theory,…

Intrinsically disordered proteins (IDPs) constitute a broad set of proteins with few uniting and many diverging properties. IDPs-and intrinsically disordered regions (IDRs) interspersed between folded domains-are generally characterized as…

We present an active learning framework for efficiently generating training data for machine-learned interatomic potentials (MLIPs). The method combines local entropy-driven molecular dynamics with global dataset-aware filtering: a…

Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of…

Machine learning interatomic potentials (MLIPs) enable efficient modeling of molecular interactions with quantum mechanical (QM) accuracy. However, constructing robust and representative training datasets that capture subtle,…

In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

This study presents a novel optimisation technique for atomic structure calculations using the Flexible Atomic Code, focussing on complex multielectron systems relevant to $r$-process nucleosynthesis and kilonova modelling. We introduce a…

Covering and elimination inequalities are central to combinatorial optimization, yet their role has largely been studied in problem-specific settings or via no-good cuts. This paper introduces a unified perspective that treats these…

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…

Machine learning interatomic potentials (MLIPs) are one of the main techniques in the materials science toolbox, able to bridge ab initio accuracy with the computational efficiency of classical force fields. This allows simulations ranging…

We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…

Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…

Random unitaries sampled from the Haar measure serve as fundamental models for generic quantum many-body dynamics. Under standard cryptographic assumptions, recent works have constructed polynomial-size quantum circuits that are…

The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behaviour…

This article reviews recent inverse statistical-mechanical methodologies that we have devised to optimize interaction potentials in soft matter systems that correspond to stable "target" structures. We are interested in finding the…

An adaptive physics-inspired model design strategy for machine-learning interatomic potentials (MLIPs) is proposed. This strategy relies on iterative reconfigurations of composite models from single-term models, followed by a unified…