arXiv subjects

Yohai Bar-Sinai

Publications and source records attributed to Yohai Bar-Sinai.

At least 19 recordsLinked to original sources

arXiv2026

Earthquake magnitudes depend on seismic history, as revealed by a neural network analysis

Earthquake occurrence is notoriously difficult to predict. While some aspects of their spatiotemporal statistics can be relatively well captured by point-process models, very little is known regarding the magnitude of future events, and it is deeply debated whether it is possible to predict the magnitude of an earthquake before it starts. Most operational forecasting models assume that earthquake magnitudes follow a time-independent Gutenberg-Richter (GR) distribution, effectively treating magnitudes as independent of seismic history. We address this fundamental question by demonstrating that standard hypocenter catalogs carry information about future earthquake magnitudes, making them more predictable than previously considered. We present MAGNET (MAGnitude Neural EsTimation model), which uses a multi-encoder neural network architecture with LSTM units to process spatiotemporal patterns in seismic history. By analyzing hypocenter locations, occurrence times, and magnitudes of past events, MAGNET generates probabilistic magnitude forecasts that demonstrate information gains in predicting magnitudes of future events over GR-based models, after controlling for detection artifacts. Our model achieves an information gain of approximately 0.07 bit per earthquake on average over the GR benchmark in Southern California, Japan, and New Zealand catalogs, with this advantage persisting. These results demonstrate that hypocentral earthquake catalogs contain extractable information about future magnitudes, challenging the conventional separability assumption in earthquake forecasting and offering new approaches for seismic hazard assessment.

physics.geo-ph↗

arXiv2025

Machine Learning the Entropy to Estimate Free Energy Differences without Sampling Transitions

Thermodynamic phase transitions, a central concept in physics and chemistry, are typically controlled by an interplay of enthalpic and entropic contributions. In most cases, the estimation of the enthalpy in simulations is straightforward but evaluating the entropy is notoriously hard. As a result, it is common to induce transitions between the metastable states and estimate their relative occupancies, from which the free energy difference can be inferred. However, for systems with large free energy barriers, sampling these transitions is a significant computational challenge. Dedicated enhanced sampling algorithms require significant prior knowledge of the slow modes governing the transition, which is typically unavailable. We present an alternative approach, which only uses short simulations of each phase separately. We achieve this by employing a recently developed deep learning model for estimating the entropy and hence the free energy of each metastable state. We benchmark our approach calculating the free energies of crystalline and liquid metals. Our method features state-of-the-art precision in estimating the melting transition temperature in Na and Al without requiring any prior information or simulation of the transition pathway itself.

cond-mat.soft↗

arXiv2025

Grokking at the Edge of Linear Separability

We investigate the phenomenon of grokking -- delayed generalization accompanied by non-monotonic test loss behavior -- in a simple binary logistic classification task, for which "memorizing" and "generalizing" solutions can be strictly defined. Surprisingly, we find that grokking arises naturally even in this minimal model when the parameters of the problem are close to a critical point, and provide both empirical and analytical insights into its mechanism. Concretely, by appealing to the implicit bias of gradient descent, we show that logistic regression can exhibit grokking when the training dataset is nearly linearly separable from the origin and there is strong noise in the perpendicular directions. The underlying reason is that near the critical point, "flat" directions in the loss landscape with nearly zero gradient cause training dynamics to linger for arbitrarily long times near quasi-stable solutions before eventually reaching the global minimum. Finally, we highlight similarities between our findings and the recent literature, strengthening the conjecture that grokking generally occurs in proximity to the interpolation threshold, reminiscent of critical phenomena often observed in physical systems.

stat.ML↗

arXiv2024

Hidden Markov modeling of single particle diffusion with stochastic tethering

The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a recent experiment, here we analyze the problem of particles undergoing two-dimensional Brownian motion with transient tethering to the surface. We model the problem as a Hidden Markov Model where the physical position is observed, and the tethering state is hidden. We develop an alternating maximization algorithm to infer the hidden state of the particle and estimate the physical parameters of the system. The crux of our method is a saddle-point-like approximation, which involves finding the most likely sequence of hidden states and estimating the physical parameters from it. Extensive numerical tests demonstrate that our algorithm reliably finds the model parameters, and is insensitive to the initial guess. We discuss the different regimes of physical parameters and the algorithm's performance in these regimes. We also provide a ready-to-use open source implementation of our algorithm.

cond-mat.soft↗

arXiv2023

Grokking in Linear Estimators -- A Solvable Model that Groks without Understanding

Grokking is the intriguing phenomenon where a model learns to generalize long after it has fit the training data. We show both analytically and numerically that grokking can surprisingly occur in linear networks performing linear tasks in a simple teacher-student setup with Gaussian inputs. In this setting, the full training dynamics is derived in terms of the training and generalization data covariance matrix. We present exact predictions on how the grokking time depends on input and output dimensionality, train sample size, regularization, and network initialization. We demonstrate that the sharp increase in generalization accuracy may not imply a transition from "memorization" to "understanding", but can simply be an artifact of the accuracy measure. We provide empirical verification for our calculations, along with preliminary results indicating that some predictions also hold for deeper networks, with non-linear activations.

stat.ML↗

arXiv2023

Charting the Topography of the Neural Network Landscape with Thermal-Like Noise

The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is to understand the geometry and topography of the landscape that guides the optimization. In this work, we employ standard Statistical Mechanics methods, namely, phase-space exploration using Langevin dynamics, to study this landscape for an over-parameterized fully connected network performing a classification task on random data. Analyzing the fluctuation statistics, in analogy to thermal dynamics at a constant temperature, we infer a clear geometric description of the low-loss region. We find that it is a low-dimensional manifold whose dimension can be readily obtained from the fluctuations. Furthermore, this dimension is controlled by the number of data points that reside near the classification decision boundary. Importantly, we find that a quadratic approximation of the loss near the minimum is fundamentally inadequate due to the exponential nature of the decision boundary and the flatness of the low-loss region. This causes the dynamics to sample regions with higher curvature at higher temperatures, while producing quadratic-like statistics at any given temperature. We explain this behavior by a simplified loss model which is analytically tractable and reproduces the observed fluctuation statistics.

cond-mat.stat-mech↗

arXiv2020

Learned discretizations for passive scalar advection in a 2-D turbulent flow

The computational cost of fluid simulations increases rapidly with grid resolution. This has given a hard limit on the ability of simulations to accurately resolve small scale features of complex flows. Here we use a machine learning approach to learn a numerical discretization that retains high accuracy even when the solution is under-resolved with classical methods. We apply this approach to passive scalar advection in a two-dimensional turbulent flow. The method maintains the same accuracy as traditional high-order flux-limited advection solvers, while using 4x lower grid resolution in each dimension. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The solver can achieve near-peak hardware utilization on CPUs and accelerators via convolutional filters. Code is available at https://github.com/google-research/data-driven-pdes.

physics.comp-ph↗

arXiv2020

Machine-learning Iterative Calculation of Entropy for Physical Systems

Characterizing the entropy of a system is a crucial, and often computationally costly, step in understanding its thermodynamics. It plays a key role in the study of phase transitions, pattern formation, protein folding and more. Current methods for entropy estimation suffer either from a high computational cost, lack of generality or inaccuracy, and inability to treat complex, strongly interacting systems. In this paper, we present a novel method, termed MICE, for calculating the entropy by iteratively dividing the system into smaller subsystems and estimating the mutual information between each pair of halves. The estimation is performed with a recently proposed machine learning algorithm which works with arbitrary network architectures that can be chosen to fit the structure and symmetries of the system at hand. We show that our method can calculate the entropy of various systems, both thermal and athermal, with state-of-the-art accuracy. Specifically, we study various classical spin systems, and identify the jamming point of a bidisperse mixture of soft disks. Lastly, we suggest that besides its role in estimating the entropy, the mutual information itself can provide an insightful diagnostic tool in the study of physical systems.

cond-mat.stat-mech↗

arXiv2019

Geometric charges and nonlinear elasticity of soft metamaterials

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability and aspects of the post-instability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical structures. Possible applications of the tools developed in this work for the study of ordered and disordered porous mechanical metamaterials are discussed.

cond-mat.soft↗

arXiv2019

Thermal conductance of one dimensional disordered harmonic chains

We study heat conduction mediated by longitudinal phonons in one dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find non-trivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that a system with strong disorder, characterized by a `heavy-tailed' probability distribution, and with large impedance mismatch between the bath and the system satisfies Fourier's law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.

cond-mat.dis-nn↗

arXiv2019

Spatiotemporal dynamics of frictional systems: The interplay of interfacial friction and bulk elasticity

Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation -- the macroscopic friction law -- and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of the macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the system's geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially-extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g. rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially-extended frictional systems.

cond-mat.soft↗

arXiv2019

Learning data driven discretizations for partial differential equations

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small scale physics. Deriving such coarse grained equations is notoriously difficult, and often \emph{ad hoc}. Here we introduce \emph{data driven discretization}, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end-to-end to best satisfy the equations on a low resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in one spatial dimension at resolutions 4-8x coarser than is possible with standard finite difference methods.

cond-mat.dis-nn↗

arXiv2019

Machine Learning in a data-limited regime: Augmenting experiments with synthetic data uncovers order in crumpled sheets

Machine learning has gained widespread attention as a powerful tool to identify structure in complex, high-dimensional data. However, these techniques are ostensibly inapplicable for experimental systems where data is scarce or expensive to obtain. Here we introduce a strategy to resolve this impasse by augmenting the experimental dataset with synthetically generated data of a much simpler sister system. Specifically, we study spontaneously emerging local order in crease networks of crumpled thin sheets, a paradigmatic example of spatial complexity, and show that machine learning techniques can be effective even in a data-limited regime. This is achieved by augmenting the scarce experimental dataset with inexhaustible amounts of simulated data of rigid flat-folded sheets, which are simple to simulate and share common statistical properties. This significantly improves the predictive power in a test problem of pattern completion and demonstrates the usefulness of machine learning in bench-top experiments where data is good but scarce.

cond-mat.soft↗

arXiv2017

Local thermal energy as a structural indicator in glasses

Identifying heterogeneous structures in glasses --- such as localized soft spots --- and understanding structure-dynamics relations in these systems remain major scientific challenges. Here we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change due to thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses --- an intrinsic signature of glassy frustration ---, anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal $ω^4$ density of states of quasi-localized low-frequency vibrational modes. When the spatial thermal energy field --- a `softness field' --- is considered, this power-law tail manifests itself by highly localized spots which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal-modes-based approach. These results offer a general, system/model-independent, physical-observable-based approach to identify structural properties of quiescent glasses and to relate them to glassy dynamics.

cond-mat.soft↗

arXiv2016

Gaussian fluctuations of spatially inhomogeneous polymers

Inhomogeneous polymers play an important role in various cellular processes, both in nature and in biotechnological applications. At finite temperatures, inhomogeneous polymers exhibit non-trivial thermal fluctuations. In a broader context, these are relatively simple examples for fluctuations in spatially inhomogeneous systems, which are less understood compared to their homogeneous counterparts. We develop a statistical theory of torsional, extensional and bending Gaussian fluctuations of inhomogeneous polymers, where the inhomogeneity is an inclusion of variable size and mechanical properties, using both continuum and discrete approaches. First, we analytically calculate the complete eigenvalue and eigenmode spectrum of the inhomogeneous polymer within a continuum field theory. In particular, we show that the wavenumber inside and outside of the inclusion is nearly linear in the eigenvalue index, with a nontrivial coefficient. Second, we solve the corresponding discrete problem, and highlight fundamental differences between the continuum and discrete spectra. In particular, we demonstrate that above a certain wavenumber the discrete spectrum changes qualitatively and discrete evanescent eigenmodes, that do not have continuum counterparts, emerge. The statistical thermodynamic implications of these differences are then explored by calculating fluctuation-induced forces associated with free-energy variations with either the inclusion properties (e.g.~inhomogeneity formed by adsorbing molecules) or with an external geometric constraint. The former, which is the fluctuation-induced contribution to the adsorbing molecules binding force, is shown to be affected by short wavelengths and thus cannot be calculated using the continuum approach. The latter, on the other hand, is shown to be dominated by long wavelength shape fluctuations and hence is properly described by the continuum theory.

cond-mat.stat-mech↗

arXiv2016

Frictional sliding without geometrical reflection symmetry

The dynamics of frictional interfaces play an important role in many physical systems spanning a broad range of scales. It is well-known that frictional interfaces separating two dissimilar materials couple interfacial slip and normal stress variations, a coupling that has major implications on their stability, failure mechanism and rupture directionality. In contrast, interfaces separating identical materials are traditionally assumed not to feature such a coupling due to symmetry considerations. We show, combining theory and experiments, that interfaces which separate bodies made of macroscopically identical materials, but lack geometrical reflection symmetry, generically feature such a coupling. We discuss two applications of this novel feature. First, we show that it accounts for a distinct, and previously unexplained, experimentally observed weakening effect in frictional cracks. Second, we demonstrate that it can destabilize frictional sliding which is otherwise stable. The emerging framework is expected to find applications in a broad range of systems.

cond-mat.mtrl-sci↗

arXiv2015

Dynamic instabilities of frictional sliding at a bimaterial interface

We study the 2D linear stability analysis of a deformable solid of a finite height $H$, steadily sliding on top of a rigid solid within a generic rate-and-state friction type constitutive framework, fully accounting for elastodynamic effects. We derive the linear stability spectrum, quantifying the interplay between stabilization related to the frictional constitutive law and destabilization related both to the elastodynamic bi-material coupling between normal stress variations and interfacial slip, and to finite size effects. The stabilizing effects related to the frictional constitutive law include velocity-strengthening friction (i.e.~an increase in frictional resistance with increasing slip velocity, both instantaneous and under steady-state conditions) and a regularized response to normal stress variations. We first consider the small wave-number $k$ limit and demonstrate that homogeneous sliding in this case is universally unstable, independently of the details of the friction law. This universal instability is mediated by propagating waveguide-like modes, whose fastest growing mode is characterized by a wave-number satisfying $k H\!\sim\!{\cal O}(1)$ and by a growth rate that scales with $H^{-1}$. We then consider the limit $k H\!\to\!\infty$ and derive the stability phase diagram in this case. We show that the dominant instability mode travels at nearly the dilatational wave-speed in the opposite direction to the sliding direction. Instability modes which travel at nearly the shear wave-speed in the sliding direction also exist in some range of physical parameters. Finally, we show that a finite-time regularized response to normal stress variations, within the framework of generalized rate-and-state friction models, tends to promote stability.

cond-mat.mtrl-sci↗

arXiv2015

On the spatial distribution of thermal energy in equilibrium

The equipartition theorem states that in equilibrium thermal energy is equally distributed among uncoupled degrees of freedom which appear quadratically in the system's Hamiltonian. However, for spatially coupled degrees of freedom --- such as interacting particles --- one may speculate that the spatial distribution of thermal energy may differ from the value predicted by equipartition, possibly quite substantially in strongly inhomogeneous/disordered systems. Here we show that for systems undergoing simple Gaussian fluctuations around an equilibrium state, the spatial distribution is universally bounded from above by $\frac{1}{2}k_BT$. We further show that in one-dimensional systems with short-range interactions, the thermal energy is equally partitioned even for coupled degrees of freedom in the thermodynamic limit and that in higher dimensions non-trivial spatial distributions emerge. Some implications are discussed.

cond-mat.stat-mech↗