arXiv subjects

Stefano Martiniani

Publications and source records attributed to Stefano Martiniani.

At least 37 records · Page 2Linked to original sources

arXiv2025

All that structure matches does not glitter

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task$\unicode{x2014}$generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains $\approx$40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms $N$, one with enantiomorphs, and two containing only identical structures but with different unit cells. We also propose new splits for datasets with polymorphs, ensuring that polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

cs.LG↗

arXiv2025

Gyromorphs: a new class of functional disordered materials

We introduce a new class of functional correlated disordered materials, termed Gyromorphs, which uniquely combine liquid-like translational disorder with quasi-long-range rotational order, induced by a ring of $G$ delta peaks in their structure factor. We generate gyromorphs in $2d$ and $3d$ by spectral optimization methods, verifying that they display strong discrete rotational order but no long-range translational order, while maintaining rotational isotropy at short range for sufficiently large $G$. Using a coupled dipoles approximation, we numerically show that these structures outperform quasicrystals, stealthy hyperuniformity, and Vogel spirals in the formation of low-index-contrast isotropic bandgaps in $2d$, for both scalar and vector waves, and open complete isotropic bandgaps in $3d$. This claim is further supported by analytical effective-medium theory and by numerical estimates of scattering mean-free paths. Finally, we introduce ``polygyromorphs'' with several rotational symmetries at different length scales (i.e., multiple rings of delta peaks), enabling the formation of multiple bandgaps in a single structure, thereby paving the way for fine control over optical properties.

cond-mat.stat-mech↗

arXiv2025

Guided Diffusion for the Discovery of New Superconductors

The inverse design of materials with specific desired properties, such as high-temperature superconductivity, represents a formidable challenge in materials science due to the vastness of chemical and structural space. We present a guided diffusion framework to accelerate the discovery of novel superconductors. A DiffCSP foundation model is pretrained on the Alexandria Database and fine-tuned on 7,183 superconductors with first principles derived labels. Employing classifier-free guidance, we sample 200,000 structures, which lead to 34,027 unique candidates. A multistage screening process that combines machine learning and density functional theory (DFT) calculations to assess stability and electronic properties, identifies 773 candidates with DFT-calculated $T_\mathrm{c}>5$ K. Notably, our generative model demonstrates effective property-driven design. Our computational findings were validated against experimental synthesis and characterization performed as part of this work, which highlighted challenges in sparsely charted chemistries. This end-to-end workflow accelerates superconductor discovery while underscoring the challenge of predicting and synthesizing experimentally realizable materials.

cond-mat.supr-con↗

arXiv2025

A geometric condition for robot-swarm cohesion and cluster-flock transition

We present a geometric design rule for size-controlled clustering of self-propelled particles. We show that active particles that tend to rotate under an external force have an intrinsic, signed parameter with units of curvature which we call curvity, that can be derived from first principles. Experiments with robots and numerical simulations show that properties of individual robots (radius and curvity) control pair cohesion in a binary system, and the stability of flocking and self-limiting clustering in a swarm, with applications in meta-materials and in embodied decentralized control.

cond-mat.soft↗

arXiv2025

A unifying approach to self-organizing systems interacting via conservation laws

We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and cycle matrices, we derive dual projection operators that decompose network fluxes and potentials. This formalism aligns with principles of non-equilibrium thermodynamics and captures a broad class of systems governed by flux-forcing relationships and local constraints. We extend this approach to collective dynamics through the PRojective Embedding of Dynamical Systems (PrEDS), which lifts low-dimensional dynamics into a high-dimensional space, enabling both replication and recovery of the original dynamics. When systems fall within the PrEDS class, their collective behavior can be effectively approximated through projection onto a mean-field space. We demonstrate the versatility of PrEDS across diverse domains, including resistive and memristive circuits, adaptive flow networks (e.g., slime molds), elastic string networks, and particle swarms. Notably, we establish a direct correspondence between PrEDS and swarm dynamics, revealing new insights into optimization and self-organization. Our results offer a general theoretical foundation for analyzing complex networked systems and for designing systems that self-organize through local interactions.

cond-mat.soft↗

arXiv2025

Open Materials Generation with Stochastic Interpolants

The discovery of new materials is essential for enabling technological advancements. Computational approaches for predicting novel materials must effectively learn the manifold of stable crystal structures within an infinite design space. We introduce Open Materials Generation (OMatG), a unifying framework for the generative design and discovery of inorganic crystalline materials. OMatG employs stochastic interpolants (SI) to bridge an arbitrary base distribution to the target distribution of inorganic crystals via a broad class of tunable stochastic processes, encompassing both diffusion models and flow matching as special cases. In this work, we adapt the SI framework by integrating an equivariant graph representation of crystal structures and extending it to account for periodic boundary conditions in unit cell representations. Additionally, we couple the SI flow over spatial coordinates and lattice vectors with discrete flow matching for atomic species. We benchmark OMatG's performance on two tasks: Crystal Structure Prediction (CSP) for specified compositions, and 'de novo' generation (DNG) aimed at discovering stable, novel, and unique structures. In our ground-up implementation of OMatG, we refine and extend both CSP and DNG metrics compared to previous works. OMatG establishes a new state of the art in generative modeling for materials discovery, outperforming purely flow-based and diffusion-based implementations. These results underscore the importance of designing flexible deep learning frameworks to accelerate progress in materials science. The OMatG code is available at https://github.com/FERMat-ML/OMatG.

cs.LG↗

arXiv2025

Emergent universal long-range structure in random-organizing systems

Self-organization through noisy interactions is ubiquitous across physics, mathematics, and machine learning, yet how long-range structure emerges from local noisy dynamics remains poorly understood. Here, we investigate three paradigmatic random-organizing particle systems drawn from distinct domains: models from soft matter physics (random organization, biased random organization) and machine learning (stochastic gradient descent), each characterized by distinct sources of noise. We discover universal long-range behavior across all systems, namely the suppression of long-range density fluctuations, governed solely by the noise correlation between particles. Furthermore, we establish a connection between the emergence of long-range order and the tendency of stochastic gradient descent to favor flat minima -- a phenomenon widely observed in machine learning. To rationalize these findings, we develop a fluctuating hydrodynamic theory that quantitatively captures all observations. Our study resolves long-standing questions about the microscopic origin of noise-induced hyperuniformity, uncovers striking parallels between stochastic gradient descent dynamics on particle system energy landscapes and neural network loss landscapes, and should have wide-ranging applications -- from the self-assembly of hyperuniform materials to ecological population dynamics and the design of generalizable learning algorithms.

cond-mat.soft↗

arXiv2025

A practical guide to machine learning interatomic potentials -- Status and future

The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3-10+ years.

cond-mat.mtrl-sci↗

arXiv2025

Absorbing state dynamics of stochastic gradient descent

Stochastic gradient descent (SGD) is a fundamental tool for training deep neural networks across a variety of tasks. In self-supervised learning, different input categories map to distinct manifolds in the embedded neural state space. Accurate classification is achieved by separating these manifolds during learning, akin to a packing problem. We investigate the dynamics of ``neural manifold packing'' by employing a minimal model in which SGD is applied to spherical particles in physical space. In this model, SGD minimizes the system's energy (classification loss) by stochastically reducing overlaps between particles (manifolds). We observe that this process undergoes an absorbing phase transition, prompting us to use the framework of biased random organization (BRO), a nonequilibrium absorbing state model, to describe SGD behavior. We show that BRO dynamics can be approximated by those of particles with linear repulsive interactions under multiplicative anisotropic noise. Thus, for a linear repulsive potential and small kick sizes (learning rates), we find that BRO and SGD become equivalent, converging to the same critical packing fraction $ϕ_c \approx 0.64$, despite the fundamentally different origins of their noise. This equivalence is further supported by the observation that, like BRO, near the critical point, SGD exhibits behavior consistent with the Manna universality class. Above the critical point, SGD exhibits a bias towards flatter minima of the energy landscape, reinforcing the analogy with loss minimization in neural networks.

cond-mat.stat-mech↗

arXiv2025

Unconditional stability of a recurrent neural circuit implementing divisive normalization

Stability in recurrent neural models poses a significant challenge, particularly in developing biologically plausible neurodynamical models that can be seamlessly trained. Traditional cortical circuit models are notoriously difficult to train due to expansive nonlinearities in the dynamical system, leading to an optimization problem with nonlinear stability constraints that are difficult to impose. Conversely, recurrent neural networks (RNNs) excel in tasks involving sequential data but lack biological plausibility and interpretability. In this work, we address these challenges by linking dynamic divisive normalization (DN) to the stability of ORGaNICs, a biologically plausible recurrent cortical circuit model that dynamically achieves DN and that has been shown to simulate a wide range of neurophysiological phenomena. By using the indirect method of Lyapunov, we prove the remarkable property of unconditional local stability for an arbitrary-dimensional ORGaNICs circuit when the recurrent weight matrix is the identity. We thus connect ORGaNICs to a system of coupled damped harmonic oscillators, which enables us to derive the circuit's energy function, providing a normative principle of what the circuit, and individual neurons, aim to accomplish. Further, for a generic recurrent weight matrix, we prove the stability of the 2D model and demonstrate empirically that stability holds in higher dimensions. Finally, we show that ORGaNICs can be trained by backpropagation through time without gradient clipping/scaling, thanks to its intrinsic stability property and adaptive time constants, which address the problems of exploding, vanishing, and oscillating gradients. By evaluating the model's performance on RNN benchmarks, we find that ORGaNICs outperform alternative neurodynamical models on static image classification tasks and perform comparably to LSTMs on sequential tasks.

q-bio.NC↗

arXiv2024

Social Physics of Bacteria: Avoidance of an Information Black Hole

Social physics explores responses to information exchange in a social network, and can be mapped down to bacterial collective signaling. Here, we explore how social inter-bacterial communication includes coordination of response to communication loss, as opposed to solitary searching for food, with collective response emergence at the population level. We present a 2-dimensional enclosed microfluidic environment that utilizes concentric rings of funnel ratchets, which direct motile E.coli bacteria towards a sole exit hole, an information ``black hole'', passage into the black hole irreversibly sweeps the bacteria away via hydrodynamic flow. We show that the spatiotemporal evolution of entropy production reveals how bacteria avoid crossing the hydrodynamic black hole information horizon.

physics.bio-ph↗

arXiv2024

On the design space between molecular mechanics and machine learning force fields

A force field as accurate as quantum mechanics (QM) and as fast as molecular mechanics (MM), with which one can simulate a biomolecular system efficiently enough and meaningfully enough to get quantitative insights, is among the most ardent dreams of biophysicists -- a dream, nevertheless, not to be fulfilled any time soon. Machine learning force fields (MLFFs) represent a meaningful endeavor towards this direction, where differentiable neural functions are parametrized to fit ab initio energies, and furthermore forces through automatic differentiation. We argue that, as of now, the utility of the MLFF models is no longer bottlenecked by accuracy but primarily by their speed (as well as stability and generalizability), as many recent variants, on limited chemical spaces, have long surpassed the chemical accuracy of $1$ kcal/mol -- the empirical threshold beyond which realistic chemical predictions are possible -- though still magnitudes slower than MM. Hoping to kindle explorations and designs of faster, albeit perhaps slightly less accurate MLFFs, in this review, we focus our attention on the design space (the speed-accuracy tradeoff) between MM and ML force fields. After a brief review of the building blocks of force fields of either kind, we discuss the desired properties and challenges now faced by the force field development community, survey the efforts to make MM force fields more accurate and ML force fields faster, envision what the next generation of MLFF might look like.

physics.chem-ph↗

arXiv2024

Element-wise and Recursive Solutions for the Power Spectral Density of Biological Stochastic Dynamical Systems at Fixed Points

Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady-state, many such processes can be described by stochastic linear time-invariant (LTI) systems driven by Gaussian white noise, whose PSD is a complex rational function of the frequency that can be concisely expressed in terms of their Jacobian, dispersion, and diffusion matrices, fully defining the statistical properties of the system's dynamics at steady-state. Here, we arrive at compact element-wise solutions of the rational function coefficients for the auto- and cross-spectrum that enable the explicit analytical computation of the PSD in dimensions n=2,3,4. We further present a recursive Leverrier-Faddeev-type algorithm for the exact computation of the rational function coefficients. Crucially, both solutions are free of matrix inverses. We illustrate our element-wise and recursive solutions by considering the stochastic dynamics of neural systems models, namely Fitzhugh-Nagumo (n=2), Hindmarsh-Rose (n=3), Wilson-Cowan (n=4), and the Stabilized Supralinear Network (n=22), as well as an evolutionary game-theoretic model with mutations (n=5, 31). We extend our approach to derive a recursive method for calculating the coefficients in the power series expansion of the integrated covariance matrix for interacting spiking neurons modeled as Hawkes processes on arbitrary directed graphs.

math.DS↗

arXiv2024

Transport and Energetics of Bacterial Rectification

Randomly moving active particles can be herded into directed motion by asymmetric geometric structures. Although such a rectification process has been extensively studied due to its fundamental, biological, and technological relevance, a comprehensive understanding of active matter rectification based on single particle dynamics remains elusive. Here, by combining experiments, simulations, and theory, we study the directed transport and energetics of swimming bacteria navigating through funnel-shaped obstacles -- a paradigmatic model of rectification of living active matter. We develop a microscopic parameter-free model for bacterial rectification, which quantitatively explains experimental and numerical observations and predicts the optimal geometry for the maximum rectification efficiency. Furthermore, we quantify the degree of time irreversibility and measure the extractable work associated with bacterial rectification. Our study provides quantitative solutions to long-standing questions on bacterial rectification and establishes a generic relationship between time irreversibility, particle fluxes, and extractable work, shedding light on the energetics of non-equilibrium rectification processes in living systems.

cond-mat.soft↗

arXiv2023

Fast Generation of Spectrally-Shaped Disorder

Media with correlated disorder display unexpected transport properties, but it is still a challenge to design structures with desired spectral features at scale. In this work, we introduce an optimal formulation of this inverse problem by means of the non-uniform fast Fourier transform, thus arriving at an algorithm capable of generating systems with arbitrary spectral properties, with a computational cost that scales $O(N \log N)$ with system size. The method is extended to accommodate arbitrary real-space interactions, such as short-range repulsion, to simultaneously control short- and long-range correlations. We thus generate the largest-ever stealthy hyperuniform configurations in $2d$ ($N = 10^9$) and $3d$ ($N > 10^7$). By an Ewald sphere construction we link the spectral and optical properties at the single-scattering level, and show that these structures in $2d$ and $3d$ generically display transmission gaps, providing a concrete example of fine-tuning of a physical property at will. We also show that large $3d$ power-law hyperuniformity in particle packings leads to single-scattering properties near-identical to those of simple hard spheres. Finally, we show that enforcing large spectral power at a small number of peaks with the right symmetry leads to the non-deterministic generation of quasicrystalline structures in both $2d$ and $3d$.

cond-mat.stat-mech↗

arXiv2023

When you can't count, sample! Computable entropies beyond equilibrium from basin volumes

In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity hinges on the knowledge of the a priori probabilities of observing the states of the system, given by the Boltzmann distribution. Unfortunately, the successes of equilibrium statistical mechanics are hard to replicate out of equilibrium, where the a priori probabilities of observing states are in general not known, precluding the naïve application of usual tools. In the last decade, exciting developments have occurred that enable the direct numerical estimation of the entropy and density of states of athermal and non-equilibrium systems, thanks to significant methodological advances in the computation of the volume of high-dimensional basins of attraction. Here, we provide a detailed account of these methods, underscoring the challenges that lie in such estimations, recent progress on the matter, and promising directions for future work.

cond-mat.stat-mech↗

arXiv2023

ColabFit Exchange: open-access datasets for data-driven interatomic potentials

Data-driven (DD) interatomic potentials (IPs) trained on large collections of first principles calculations are rapidly becoming essential tools in the fields of computational materials science and chemistry for performing atomic-scale simulations. Despite this, apart from a few notable exceptions, there is a distinct lack of well-organized, public datasets in common formats available for use with IP development. This deficiency precludes the research community from implementing widespread benchmarking, which is essential for gaining insight into model performance and transferability, and also limits the development of more general, or even universal, IPs. To address this issue, we introduce the ColabFit Exchange, the first database providing open access to a large collection of systematically organized datasets from multiple domains that is especially designed for IP development. The ColabFit Exchange is publicly available at \url{https://colabfit.org/}, providing a web-based interface for exploring, downloading, and contributing datasets. Composed of data collected from the literature or provided by community researchers, the ColabFit Exchange currently (September 2023) consists of 139 datasets spanning nearly 70,000 unique chemistries, and is intended to continuously grow. In addition to outlining the software framework used for constructing and accessing the ColabFit Exchange, we also provide analyses of the data, quantifying the diversity of the database and proposing metrics for assessing the relative diversity of multiple datasets. Finally, we demonstrate an end-to-end IP development pipeline, utilizing datasets from the ColabFit Exchange, fitting tools from the KLIFF software package, and validation tests provided by the OpenKIM framework.

cond-mat.mtrl-sci↗

arXiv2023

Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in $d=3$ dimensions, and thus obtain an estimate of the random close packing (RCP) volume fraction, $ϕ_{\textrm{RCP}}$, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations, using both our own and results reported in previous works, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity, using three different particle size distributions, namely the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions, when using as reference our own simulations and results from the literature. In particular, we find $ϕ_{\textrm{RCP}}$ to increase monotonically with the relative standard deviation, $s_σ$, of the distribution, and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for $ϕ_{\textrm{RCP}}$ that quantitatively captures a distribution-independent regime for $s_σ < 0.5$. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.

cond-mat.soft↗