New estimates for Hitchin's equations at high energy.
problem Solutions to Hitchin's self-duality equations at high energy.
method New estimates and asymptotic decoupling phenomenon.
result Generalization to arbitrary Higgs bundles.
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48 results for “high energy spaces”
Consensus-based adaptive sampling and approximation for high-dimensional energy landscapesphysics.comp-ph
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
The paper defines a complete geodesic metric for high energy spaces in Kähler manifolds.
problem Defining a metric for high energy spaces in Kähler manifolds.
method Endowing the high energy space with a metric that makes it a complete geodesic metric space.
result The geodesic metric space is uniformly convex for .
L-GATr transforms high-energy physics data using geometric algebra and Lorentz symmetry.
problem Extracting scientific understanding from particle-physics experiments with high precision and efficiency.
method L-GATr, a geometric algebra Transformer, representing data in 4D space-time and being equivariant under Lorentz transformations.
result L-GATr achieves performance comparable to or better than domain-specific baselines on regression, classification, and generative tasks.
In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based on two energies measuring the area distortion and the angle distortion of a quasiconformal homeomorphism. We show that the energy minimizer …
Before any publication, data analysis of high-energy physics experiments must be validated. This validation is granted only if a perfect understanding of the data and the analysis process is demonstrated. Therefore, physicists prefer using transparent machine learning algorithms whose performances highly rely on the su…
Versatile model for High Energy Physics events.
problem Modeling complex interactions in high-energy physics data.
method Energy-based probabilistic model with multi-purpose architecture.
result Achieves success in diverse applications like simulation, anomaly detection, and particle identification.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recentl…
We extend Vasy's results on semiclassical high energy estimates for the meromorphic continuation of the resolvent for asymptotically hyperbolic manifolds to metrics that are not necessarily even. Vasy's method gives the meromorphic continuation of the resolvent and high energy estimates in strips, assuming that the geo…
Machine Learning algorithms based on Brain-inspired Hyperdimensional(HD) computing imitate cognition by exploiting statistical properties of high-dimensional vector spaces. It is a promising solution for achieving high energy efficiency in different machine learning tasks, such as classification, semi-supervised learni…
Paper proposes a method to improve MCMC sampling for energy-based models.
problem MCMC sampling of energy-based models is often not mixing in high-dimensional data.
method Proposes using a flow-based model as a backbone to correct the energy-based model, enabling mixing in latent space.
result MCMC sampling of the corrected EBM in the latent space mixes well and traverses modes in the data space.
Defines weak normals for irregular curves in high-dimensional spaces.
problem Dealing with irregular curves in high-dimensional Euclidean spaces.
method Using sequences of inscribed polygonals and Gram-Schmidt procedure, introduces a relaxed notion of weak normals.
result Weak normals for irregular curves are the strong limit of approximating polygonals and agree with relaxed energy.
Study shows energy levels on hyperbolic surfaces follow GOE fluctuations.
problem Understanding energy level fluctuations on hyperbolic surfaces.
method Analysis of Laplace eigenvalues on hyperbolic surfaces, using GOE random matrix theory.
result Energy variance on typical hyperbolic surfaces closely matches GOE fluctuations.
GEBM combines energy function and base distribution for better generative modeling.
problem Improving generative models with better quality samples and performance.
method Alternating training between energy function and base distribution, using MCMC for sampling.
result GEBMs produce higher quality samples and better performance than GANs.
Modern Hopfield networks help prevent forgetting in generative models after task changes.
problem How to prevent forgetting in generative models after task changes.
method Introduce intrinsic forgetting as an increase in Hopfield energy after task change, analyze memory replay effectiveness, and validate predictions in experiments.
result High-energy, outlier-like samples are more forgettable than cluster-like samples, and energy-based selection of replay samples mitigates forgetting.
Machine Learning (ML) algorithms, like Convolutional Neural Networks (CNN), Support Vector Machines (SVM), etc. have become widespread and can achieve high statistical performance. However their accuracy decreases significantly in energy-constrained mobile and embedded systems space, where all computations need to be c…
This work optimizes statistical inference with neural networks for high-energy physics data.
problem Optimal dimensionality reduction with minimal loss of information in the presence of systematic uncertainties.
method Neural network optimization based on binned Poisson likelihoods with nuisance parameters.
result Estimates of parameters of interest close to optimal.
Gradient estimation techniques applied to programs with randomness in high energy physics.
problem Differentiating programs with discrete randomness in high energy physics.
method Several gradient estimation techniques, including Stochastic AD method, applied to simplified detector design experiments.
result Development of the first fully differentiable branching program.
Paper proposes a method to design molecules with specific properties.
problem Designing molecules with desired chemical and biological properties.
method Energy-based model in latent space, SGDS algorithm for gradual distribution shifting.
result Method achieves strong performances on various molecule design tasks.
Study on -surfaces in negatively curved 3-manifolds, focusing on energy and entropy.
problem Understanding the growth rate and asymptotic behavior of -surfaces in negatively curved 3-manifolds.
method Proved results on the asymptotic behavior of high energy -surfaces, including upper bounds and rigidity theorems.
result Determined a rigid upper bound for the growth rate of quasi-Fuchsian -surfaces in negatively curved 3-manifolds.
CESAR improves wind speed and power forecasting for high-resolution simulations.
problem Accurate high-resolution wind forecasting for efficient power grid management.
method A spatio-temporal neural network model using deep convolutional autoencoder and echo state network.
result CESAR provides up to 17% improvement in wind speed and power forecasting compared to best alternatives.
This paper tackles sampling issues in latent space EBMs by introducing diffusion-based amortization.
problem Degenerate MCMC sampling quality hinders latent space EBM learning and generation quality.
method Introduces diffusion-based amortization for long-run MCMC sampling.
result The learned amortization of MCMC is a valid long-run MCMC sampler.
GOE statistics emerge from surface moduli space averages.
problem Understanding spectral statistics on hyperbolic surfaces.
method Defined a smooth linear statistic, averaged over moduli space, and analyzed variance.
result GOE statistics are recovered in the large genus and high energy limits.
Experimental fractal landscape dynamics observed in emulsions.
problem Understanding anomalous motions in soft glassy materials.
method Quantitative analysis of oil droplet trajectories in dense emulsions.
result Experimental fractal geometry matches computational model of soft glassy dynamics.
We introduce the "Energy-based Generative Adversarial Network" model (EBGAN) which views the discriminator as an energy function that attributes low energies to the regions near the data manifold and higher energies to other regions. Similar to the probabilistic GANs, a generator is seen as being trained to produce con…
Paper generates full events from partons using machine learning.
problem Challenges of multiplicity variations between parton and reconstructed object spaces.
method Employing transformers, score-based models, and normalizing flows.
result Achieves remarkably accurate results in generating full events.
In this paper we describe a new method for analyzing the Laplacian on asymptotically hyperbolic spaces, which was introduced recently by the author. This new method in particular constructs the analytic continuation of the resolvent for even metrics (in the sense of Guillarmou), and gives high energy estimates in strip…
Quantum mechanics applied to option pricing with a time-dependent bubble.
problem Option pricing with a time-dependent arbitrage bubble.
method Application of Dirac's interaction picture to the Black-Scholes equation.
result Exact and approximate solutions for option pricing with a square bubble.
A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.
problem Optimization challenges in non-convex loss functions and machine learning tasks.
method Discretization of Born-Infeld dynamics for energy-conserving Hamiltonian optimization.
result The method avoids high local minima and outperforms traditional methods in shallow valleys.
LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.
problem Limitations of specialized layers in Lorentz-equivariant neural networks.
method LLoCa framework using local reference frames and geometric message passing.
result Models achieve competitive and state-of-the-art accuracy on particle physics tasks.
Delaunay tori minimize Willmore energy under isoperimetric constraints.
problem Finding minimizers of the Willmore energy under isoperimetric constraints.
method Constructing Delaunay tori using complete elliptic integrals and analyzing their Willmore energy.
result Existence of smoothly embedded tori minimizing the Willmore functional under isoperimetric constraints.
Study magnetic Laplacians on hyperbolic surfaces, revealing three regimes of eigenfunction behavior.
problem Investigate semiclassical defect measures of magnetic Laplacians on hyperbolic surfaces.
method Analyze eigenfunctions in low, critical, and high energy regimes using quantum ergodicity and equidistribution.
result Eigenfunctions in different regimes converge to distinct measures: invariant, Liouville, or equidistributed.
Adversarial domain adaptation reduces sample bias in high energy physics classifier.
problem Sample bias in high energy physics classifier training.
method Adversarial domain adaptation using neural networks with gradient reversal layer.
result Successful bias removal on simulated events at the LHC.
Machine learning in high-energy physics faces challenges from nuisance parameters, which are reviewed and techniques to mitigate their impact are discussed.
problem Impact of nuisance parameters on machine learning performance in high-energy physics.
method Review and discussion of techniques including nuisance-parameterized models, modified or adversary losses, semi-supervised learning, and inference-aware techniques.
result Various methods to reduce the impact of nuisance parameters and improve model performance in high-energy physics.
Relative energy gap for harmonic maps of Riemann surfaces into real analytic Riemannian manifoldsmath.AP
We extend the well-known Sacks-Uhlenbeck energy gap result (1981) for harmonic maps from closed Riemann surfaces into closed Riemannian manifolds from the case of maps with small energy (thus near a constant map), to the case of harmonic maps with high absolute energy but small energy relative to a reference harmonic m…
A common problem in a high energy physics experiment is extracting a signal from a much larger background. Posed as a classification task, there is said to be an imbalance in the number of samples belonging to the signal class versus the number of samples from the background class. In this work we provide a brief overv…
This paper presents a method to obtain geometric registrations between high-genus () surfaces. Surface registration between simple surfaces, such as simply-connected open surfaces, has been well studied. However, very few works have been carried out for the registration of high-genus surfaces. The high-genus t…
Quantum hybrid vision transformers improve event classification in high energy physics.
problem Excessive computational resources for training and deploying vision transformer models.
method Constructed quantum hybrid vision transformers for high energy physics event classification.
result Quantum hybrid models achieve comparable performance to classical models with fewer parameters.
This paper addresses the energy disaggregation problem, i.e. decomposing the electricity signal of a whole home to its operating devices. First, we cast the problem as a dictionary learning (DL) problem where the key electricity patterns representing consumption behaviors are extracted for each device and stored in a d…
The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M-dimensional manifold in N-dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M…
Modeling wind dynamics in Saudi Arabia using deep learning and stochastic PDEs.
problem Accurately modeling spatio-temporal wind patterns in a large, diverse, and understudied region.
method Energy distance-based spatial reduction, sparse stochastic Echo State Network, non-stationary stochastic PDE reconstruction.
result Produces more accurate wind speed and energy forecasts, saving $1 million annually.
Risk-Aware Energy Scheduling for Edge Computing with Microgrid: A Multi-Agent Deep Reinforcement Learning Approachphysics.soc-ph
In recent years, multi-access edge computing (MEC) is a key enabler for handling the massive expansion of Internet of Things (IoT) applications and services. However, energy consumption of a MEC network depends on volatile tasks that induces risk for energy demand estimations. As an energy supplier, a microgrid can fac…
Study on infinite energy maps from surfaces to CAT(0) spaces.
problem Harmonic maps with infinite energy from Riemann surfaces to CAT(0) spaces.
method Estimates of energy growth near punctures, proof of uniqueness.
result Precise estimates of energy growth near punctures and proof of uniqueness of harmonic maps.
ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.
problem Predicting stable or metastable crystal structures of large systems.
method Noniterative screening using transfer learning and generative models.
result ShotgunCSP achieves 93.3% accuracy in benchmark tests with 90 different crystal structures.
Study shows TAP free energy minimization provides better posterior inference in high-dimensional linear models.
problem Deviation from true posterior mean and underestimation of posterior uncertainty in variational inference.
method Minimization of TAP free energy in a high-dimensional asymptotic framework, showing geometric and statistical properties.
result Local minimizer of TAP free energy provides consistent estimate of posterior marginals and correctly calibrated posterior inference.
The paper extends graph-based semi-supervised learning to infinite-dimensional Wasserstein space.
problem Graph-based semi-supervised learning in high-dimensional data.
method Laplace Learning in the Wasserstein space, proving variational convergence and characterizing the Laplace-Beltrami operator.
result Consistent classification performance in high-dimensional settings.
The paper proposes a thermodynamic potential to guide training of generative models, breaking ergodicity to improve functionality.
problem Improving generative model functionality while limiting access to underrepresented patterns.
method Constructing a thermodynamic potential that guides training, leading to multiple minima in the free energy.
result Training a generative model breaks ergodicity, preventing escape into the high-temperature phase.