Higher topos theory applied to physics.
problem No specific problem stated.
method Exposition of higher topos theory.
result No specific key result mentioned.
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48 results for “higher physics”
-Bundlesmath.AT
This article reviews -bundles and their applications in geometry and physics.
problem Understanding higher bundles in geometry and physics.
method An -categorical formulation of higher bundles.
result Identification of higher bundles in various contexts.
Higher Gauge Theoryhep-th
Survey on advanced gauge theory concepts.
problem Understanding higher gauge theory structures.
method Introduction to higher structures and connections on higher principal bundles.
result Summarized applications and principles of higher gauge theories.
After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra cohomology: a brief introduction 4. Symmetric polynomials and higher order cocycles 5…
Parametric model reduction of mean-field and stochastic systems via higher-order action matchingstat.ML
This work learns models for population dynamics using variational methods and higher-order quadrature.
problem Modeling population dynamics of physical systems with stochastic and mean-field effects.
method Variational problem to infer gradient fields, combining Monte Carlo sampling with higher-order quadrature rules.
result Accurate prediction of population dynamics over a wide range of parameters.
Study finds physical momentum portfolios in Indian stock market yield higher returns than benchmarks.
problem Determining abnormal returns for physical momentum portfolios in the Indian stock market.
method Constructed physical momentum portfolios for daily, weekly, monthly, and yearly timescales, evaluated historical returns and risk profiles.
result Daily time scale physical momentum portfolios showed the strongest reversal with a 16-fold profit.
ξ-torch simplifies physics-informed learning by providing differentiable functionals.
problem Training physics-informed deep neural networks requires differentiable physical simulations.
method ξ-torch offers a library of differentiable functionals for scientific simulations.
result Improves numerical stability and reduces memory requirements for higher order derivatives.
(K)not machine learninghep-th
Machine learning knot invariants with physics applications.
problem Understanding relations between knot invariants in physics.
method Machine learning and theoretical physics (Chern-Simons theory, gauge theories).
result New analytic results from Big Data experiments.
Physics-informed diffusion model detects anomalous trajectories in GPS data.
problem Detecting fake GPS trajectories in international waters.
method Physics-informed diffusion model integrating kinematic constraints.
result Higher prediction accuracy and lower error rate for anomaly detection.
We construct a parallel transport on higher loop spaces of a manifold in term of a higher dimensional generalization of iterated path integrals. Under mild assumptions, we define a de Rham complex on higher loop spaces and we recover a known result of Hain of a de Rham structure on higher homotopy groups of a manifold.…
Many physical theories, including notably string theory, require non-abelian higher gauge fields defining higher holonomy. Previous approaches to such higher connections on categorified principal bundles require these to be fake flat. This condition, however, renders them locally gauge equivalent to connections on abel…
Study on higher-dimensional black holes, focusing on retractions and scalar quasibound states.
problem Examining the physics of a five-dimensional non-extremal Reissner-Nordström black hole.
method Analyzing the line element and scalar field perturbations using polynomial conditions of Heun functions.
result Obtained analytical expressions for quasibound state frequencies and discussed system stability.
The work proposes a geometric background of the theory of field interactions and strings in spaces with higher order anisotropy. Our approach proceeds by developing the concept of higher order anisotropic superspace which unifies the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagra…
In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition of various algebroids as well as of Dirac structures, a joint generalization of…
New method bypasses assumptions for unbiased estimation of complex system interactions.
problem Inferring pair-wise and higher-order interactions from observational data.
method Cross-disciplinary approach using Targeted Learning for unbiased estimation.
result Universal estimator of all-order symmetric interactions without parametric assumptions.
New model learns better policies from expert demonstrations with higher efficiency.
problem Learning accurate policies from expert demonstrations with high efficiency.
method Generative adversarial imitation learning (GAIL) model that learns -divergence automatically.
result Learns better policies with higher data efficiency in physics-based control tasks.
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier work. Examples of higher derived brackets naturally appear in geometry and mathem…
Unified view of spectral networks linking geometry and gauge theory.
problem Understanding BPS states in gauge theories.
method Unified geometric and physical approaches, focusing on spectral networks.
result Spectral networks provide a framework for determining BPS spectra.
Variationality of conformal geodesics fails in higher dimensions.
problem The variationality of conformal geodesics in higher dimensions.
method Analysis of conformal geodesics in three and higher dimensions.
result Variationality fails in both parametrized and un-parametrized conformal geodesics in higher dimensions.
Physics-consistent method improves seismic inversion accuracy.
problem Challenges in seismic full-waveform inversion (FWI) due to ill-posedness and high cost.
method Hybrid approach combining physics-based models with data-driven methodologies, incorporating physics into data augmentation.
result Physics-consistent data-driven inversion yields higher accuracy and better generalization.
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.
String structures have played an important role in algebraic topology, via elliptic genera and elliptic cohomology, in differential geometry, via the study of higher geometric structures, and in physics, via partition functions. We extend the description of String structures from connected covers of the definite-signat…
MPP trains a transformer to predict multiple physical systems, improving accuracy across various tasks.
problem Training models for specific physical systems is inefficient and requires fine-tuning.
method MPP trains a shared transformer on multiple heterogeneous physical systems, projecting fields into a shared embedding space.
result A single MPP-pretrained transformer outperforms task-specific models on all pretraining sub-tasks and downstream tasks.
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this notion and other related ones to systems of higher-order differential equations …
Paper develops a new model for forecasting ocean currents.
problem Forecasting the Loop Current and its eddies for the Gulf of Mexico.
method Physics-informed Tensor-train ConvLSTM, incorporating prior physical knowledge.
result PITT-ConvLSTM outperforms state-of-the-art methods in volumetric velocity forecasting.
This work explores symplectic structures on graded manifolds and higher Lie groupoids.
problem Understanding symplectic structures on graded manifolds and their global counterparts.
method Introduction and study of graded manifolds, symplectic Q-manifolds, higher Lie groupoids, and their symplectic structures.
result Developed a graded analogue of Weinstein's tubular neighborhood theorem and explored its applications.
I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in 2-dimensions. I then present recent results obtain…
Novel approach uses inductive biases for semiconductor etching.
problem Significant violations of physics in etching process predictions.
method Introduced deep learning model with inductive biases.
result Fits measurements faster and follows physical behavior.
Extends Chern character to non-abelian cohomology, linking to physics.
problem Generalizing Chern character to non-abelian cohomology.
method Leveraging dg-algebraic rational homotopy theory and de Rham theorem.
result Generalizes Chern-Dold character, Chern-Weil homomorphism, and Cheeger-Simons homomorphism.
Paper constructs exotic spacetimes with same physical properties.
problem Whether two topologically identical manifolds can have different geometries.
method Computational approach to produce physical models on exotic spheres.
result Lorentzian metrics on homeomorphic but not diffeomorphic manifolds with same physical properties.
There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach emerged from physics and includes the orbifold Euler characteristic and its higher…
A good feature representation is a determinant factor to achieve high performance for many machine learning algorithms in terms of classification. This is especially true for techniques that do not build complex internal representations of data (e.g. decision trees, in contrast to deep neural networks). To transform th…
We consider few-body bound state systems and provide precise definitions of Borromean and Brunnian systems. The initial concepts are more than a hundred years old and originated in mathematical knot-theory as purely geometric considerations. About thirty years ago they were generalized and applied to the binding of sys…
Combines higher complex structures with flat connections to link to -algebras.
problem Linking higher complex structures to -algebras via flat connections.
method Introduces -parabolic connections and studies their curvature.
result Establishes a direct link between flat connections and higher complex structures.
We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of Gromov-Witten invariants of one-pointed maps. In genus zero, an equivariant ver…
On Gauss-Bonnet Curvaturesmath.DG
The -th Gauss-Bonnet curvature is a generalization to higher dimensions of the -dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for . The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known a…
In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger stretch tensor in a Gaussian process. We then consider an improvement on this a…
Introduces principal bundles in a new geometric category.
problem No specific problem stated; introduces a new geometric category.
method Introduces -manifolds and principal bundles within this category.
result Fundamental properties of classical principal bundles can be generalized to -manifolds.
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theo…
Neural networks learn higher-order derivatives for physics problems.
problem Lack of higher-order derivatives in neural networks for theoretical physics.
method Graph-theoretical approach to assign diagrams to partial derivatives, iterative NN perturbation theory.
result NNs can learn higher-order derivatives, improving machine-learned approximations.
The paper improves ODE solvers by integrating diverse information types.
problem Improving accuracy and physical meaningfulness of ODE solutions.
method Leveraging probabilistic solvers to include second-order information and physical conservation laws.
result Solutions become more accurate and physically meaningful with additional information.
Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning frameworkphysics.flu-dyn
Improved method using filtered PDEs for robust physics-informed deep learning.
problem Complex real-world problems with noisy and sparse data.
method Proposed a surrogate constraint (FPDE) to filter and reduce the influence of noisy and sparse observation data.
result FPDE models converge better and produce higher quality solutions with less data.
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The …
Foundation models outperform supervised methods in time series forecasting across various operational regimes.
problem Lack of domain-specific training and ongoing maintenance in supervised learning for time series forecasting.
method Evaluation of foundation models against standard supervised approaches across four operational regimes: periodic, physically constrained, stochastic, and demand forecasting.
result Foundation models are optimal for cold-start or long-tail scenarios and perform well in domains with transferable periodic structures.
By developing a generalized cobordism theory, we explore the higher global symmetries and higher anomalies of quantum field theories and interacting fermionic/bosonic systems in condensed matter. Our essential math input is a generalization of Thom-Madsen-Tillmann spectra, Adams spectral sequence, and Freed-Hopkins's t…
Training neural networks under physical constraints using a stochastic augmented Lagrangian approachphysics.comp-ph
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
DeepSVM learns SVMs without PDE solving, achieving high pricing accuracy.
problem Computational bottleneck in real-time calibration of stochastic volatility models.
method Physics-informed Deep Operator Network (PI-DeepONet) that enforces terminal payoffs and no-arbitrage conditions.
result DeepSVM achieves high pricing accuracy across various market dynamics.
A Quasilinear Algorithm for Computing Higher-Order Derivatives of Deep Feed-Forward Neural Networkscs.LG
A new algorithm speeds up neural network derivative calculations.
problem Exponential runtime of autodifferentiation for high-order derivatives in neural networks.
method n-TangentProp, a quasilinear algorithm for computing higher-order derivatives.
result Computes exact derivatives in quasilinear time, not exponential.