Single model learns physics from diverse data.
problem Lack of universal physics models for diverse applications.
method General Physics Transformer (GPhyT) trained on diverse physics data.
result Single model achieves superior performance across multiple physics domains.
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.
Foundation models trained on collider data improve jet generation tasks.
problem Improving foundation models for jet generation tasks.
method Pre-training OmniJet-α model on AspenOpenJets dataset. result Pre-trained model improves performance on jet generation tasks with domain shift.
AI model enhances grid monitoring with synchro-waveform tech.
problem Dynamic, stochastic, low-inertia future grids need advanced monitoring.
method AI Foundation Model with synchro-waveform tech.
result Significantly improved fault detection accuracy and speed.
Paper introduces TS-GPT for engineering time series forecasting.
problem Engineering time series require causal operations, unlike linguistic data.
method Innovations representation theory, Generative Pre-trained Transformer.
result TS-GPT effectively forecasts real-time locational marginal prices.
Physical foundations for relativistic spacetimes are revisited, in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of Special Relativity and Classical Mechanics) are shown to correspond with a double linear approximation in the measur…
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous foundation to modern dynamics, as well as field and gauge theories in physics, engi…
Physics-informed machine learning models improve biomolecular system simulations.
problem Modeling unresolved interactions beyond classical force fields.
method Physics-informed neural networks and operator learning.
result Accurate, mechanistic, generalizable models for long-timescale kinetics.
We give a survey of our joint ongoing work with Ali Chamseddine, Slava Mukhanov and Walter van Suijlekom. We show how a problem purely motivated by "how geometry emerges from the quantum formalism" gives rise to a slightly noncommutative structure and a spectral model of gravity coupled with matter which fits with expe…
Hybrid model combines physics and data to handle incomplete systems.
problem Incomplete physics models with missing terms.
method Combines deep grey-box models with Optimal Transport.
result Enhances incomplete physics models with superior performance.
Foundation models fail to preserve continuous geometry, identified as the Geometric Alignment Tax.
problem Continuous geometry is lost in foundation models due to discrete categorical bottlenecks.
method Controlled ablations on synthetic systems and evaluation of 14 biological models using rate-distortion theory and MINE.
result Replacing cross-entropy with a continuous head reduces geometric distortion by up to 8.5x.
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the action principle to define the conservation law for such general fields. By con…
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.
New framework for noncommutative Carrollian geometry using Lie-Rinehart pairs.
problem Developing a geometric framework for ultra-relativistic physics in noncommutative settings.
method Using ρ-Lie-Rinehart pairs to generalize Carrollian Lie algebroids to almost commutative geometry.
result Foundational principles of Carrollian geometry hold in almost commutative geometry.
These lecture notes in the De Rham-Hodge theory are designed for a 1-semester undergraduate course (in mathematics, physics, engineering, chemistry or biology). This landmark theory of the 20th Century mathematics gives a rigorous foundation to modern field and gauge theories in physics, engineering and physiology. The…
Mathematical advances needed for Digital Twins, differing from traditional models.
problem Foundational mathematical advances required for Digital Twins.
method Multi-scale, multi-physics modeling and coupling, different reliability criteria and uncertainty assessments.
result AI/ML methods can perform well in biomedical problems but fail in simple engineering systems.
Cold-start PV forecasting uses synthetic histories to train time-series foundation models.
problem Cold-start PV forecasting
method Zero-shot pipeline with synthetic histories
result TabPFN-TS achieves the lowest error under Real Feedback strategy
Neural SVEs model complex systems with memory, outperforming traditional methods.
problem Modeling systems with memory effects and irregular behavior.
method Introducing neural stochastic Volterra equations as a physics-inspired architecture.
result Neural SVEs outperform neural SDEs and DeepONets in various applications.
Develops derived differential geometry for supermanifolds.
problem Handling non-transverse intersections and singular moduli problems in geometry and physics.
method Extends existing work on derived manifolds to supergeometric and infinite-dimensional contexts.
result Establishes foundational results relating derived differential geometry to differential operators and PDE theory.
Unified Bayesian PINN framework for solving inverse problems in infrared image processing.
problem Solving inverse problems in high-dimensional settings with complex physics.
method Bayesian Physics-Informed Neural Networks (BPINN-IP) framework, incorporating physical laws and uncertainties.
result Unified framework for physical constraints, prior knowledge, and data-driven inference with uncertainty quantification.
CViT learns complex physical systems using vision transformer techniques.
problem Learning maps between infinite-dimensional function spaces in scientific machine learning.
method Combines vision transformer encoder, grid-based coordinate embedding, and cross-attention mechanism.
result Achieves state-of-the-art performance on multiple benchmarks, often surpassing larger models.
FaIRGP model improves climate emulation with physical interpretability.
problem Lack of physical interpretability in data-driven emulators.
method Bayesian approach to a data-driven emulator of energy balance equations.
result Demonstrates skillful emulation of global and spatial surface temperatures.
Optimal transport calibrates machine learning models for particle physics simulations.
problem Discrepancies between simulation and experimental data limit machine learning effectiveness.
method A model calibration approach based on optimal transport applied to high-dimensional simulations.
result Calibrated high-dimensional representations enable proper calibration of various downstream quantities.
Develops PAC-Bayesian framework for physics-informed machine learning.
problem Lack of statistical generalisation understanding for PIML models.
method PAC-Bayesian framework with multi-task perspective, incorporating physical structure.
result High-probability generalisation guarantees with unbounded losses.
Revises mean-field theory of Santa Fe model using kinetic theory.
problem Deriving a solid mathematical foundation for the Santa Fe model.
method Systematic derivation of BBGKY hierarchy from exact master equation.
result Explicit and closed-form solutions for mean-field equations.
Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple models and model identification strategies. If the modeling accuracy using phys…
Unified geometry for relativity and beyond.
problem Unified geometric framework for relativity and beyond.
method Unified Lorentz-Finsler geometry.
result Unified framework for relativity and beyond.
Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…
In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in th…
Enhances neural network solvers for PDEs with complex boundary conditions.
problem Challenges in solving PDEs with high accuracy and complex boundary conditions.
method Integrates natural gradient optimization with numerical time-stepping schemes to enforce Dirichlet boundary conditions.
result Superior accuracy and computational efficiency of the proposed methods for solving PDEs.
While model-based deep reinforcement learning (RL) holds great promise for sample efficiency and generalization, learning an accurate dynamics model is often challenging and requires substantial interaction with the environment. A wide variety of domains have dynamics that share common foundations like the laws of clas…
Physics-informed neural networks and neural operators speed up solving parametric PDEs by orders of magnitude.
problem Solving PDEs for varying parameters is computationally expensive.
method Physics-informed neural networks and neural operators learn solution mappings across parameter spaces.
result Neural operators achieve computational speedups of 10^3 to 10^5 times faster than traditional methods.
Paper proposes ExsdHawkes to model LOBs, capturing volatility dynamics.
problem Modeling volatility signature plots in LOBs with high-frequency trading dynamics.
method Extended State-Dependent Hawkes Process (ExsdHawkes) with relaxed constraints.
result ExsdHawkes uniquely reproduces volatility signature plots, identifying MLOs as catalysts.
Foundations of derived geometry in smooth settings.
problem Building tools for moduli spaces in differential geometry.
method Abstract structured spaces and universal properties in (∞,2)-categories. result Established derived flatness results for derived C∞-rings. Research proves unique continuation for Einstein-vacuum equations on aAdS spacetimes.
problem Establishing rigorous mathematical statements for AdS/CFT correspondence.
method Novel Carleman estimates and unique continuation results for wave equations on aAdS spacetimes.
result Proved a unique continuation result for the Einstein-vacuum equations from aAdS conformal boundaries.
Paper reconciles two methods of describing Riemannian spaces.
problem Riemann's length principle and Klein's equality principle in geometry.
method Group-theoretic approach to unify length and equality principles.
result Unified group of diffeomorphisms and gauge rotations for Riemannian spaces.
Recent advances in deep learning motivate the use of deep neural networks in Internet-of-Things (IoT) applications. These networks are modelled after signal processing in the human brain, thereby leading to significant advantages at perceptual tasks such as vision and speech recognition. IoT applications, however, ofte…
Recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the Brownian motion has played the key role as in physics. In our previous report (arXiv:1703.06739; to appear in Phys. Rev. Lett.), we have prese…
Develops a new model for pricing without arbitrage opportunities.
problem Arbitrage opportunities in standard jump-diffusion models.
method Introduces a multi-type jump-diffusion model with diffusion-dependent jumps.
result Derives no-arbitrage condition linking drift to model parameters.
AIF improves physical AI agents' performance in dynamic environments.
problem Physical AI agents are less capable than biological agents in open-ended real-world environments.
method Developed from probability theory, Bayesian machine learning, variational inference, and Active Inference (AIF), grounded in the Free Energy Principle.
result AIF minimizes variational free energy and is well-suited to physical constraints.
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innov…
Analyzes the concept of fields in classical and quantum physics.
problem Challenges in defining fields in classical and quantum physics.
method Uses groupoid description of quantum mechanics and categorical language.
result Fields as functors among groupoids of test particles and intrinsic system nature.
Survey and new results link hydrodynamics, molecular physics, and financial engineering.
problem Understanding financial engineering topics like Asian options and volatility swaps.
method Linking Kevin waves, Klein-Kramers, and Kolmogorov equations to financial models.
result Corrected the original solution of the Kolmogorov equation.
A new framework uses uncertainty to learn from raw data without explicit models.
problem Limitations of traditional machine learning models and lack of interpretability.
method Introduces a model-free framework using surprisal (information theoretic uncertainty) to analyze and infer from raw data.
result Achieves at or near state-of-the-art performance across various machine learning tasks.
Survey of financial foundation models for diverse applications.
problem Challenges in applying general-purpose FMs to financial tasks.
method Review of financial foundation models (FFMs) in three modalities.
result Emergence of FFMs designed specifically for finance.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Time series foundation models are well-calibrated, improving over baseline models.
problem Calibration of time series foundation models for practical applications.
method Systematic evaluations of five time series foundation models and two baselines, assessing calibration, prediction heads, and long-term forecasting.
result Time series foundation models are consistently better calibrated than baseline models and do not show over- or under-confidence.
Introduces foundation priors for using model-generated data in empirical research.
problem Using model-generated data as real observations in empirical research.
method Introduces foundation priors as an exponential-tilted, generalized Bayesian update of the user's primitive prior.
result Synthetic data reflects both model patterns and user's priors, enabling principled use in empirical work.