The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
New model combines physics and machine learning for ocean dynamics.
problem Discovering hidden laws governing ocean dynamics.
method Develops Deep Neural Numerical Models (DNNMs) to learn hidden variables of physical laws.
result Illustrates DNNMs applied to Sea Surface Height dynamics, connecting to QG model.
Bayesian model learns physics laws from data with uncertainty quantification.
problem Lack of uncertainty in discovering governing physical laws from data.
method Bayesian approach with leaf and root modules, Gaussian process for operators, automatic differentiation.
result Quantifies reliability of learned physics laws and propagates uncertainty.
Study on generalisation in random feature learning and hidden manifold models.
problem Generalisation in high-dimensional learning problems.
method Replica method from statistical physics for asymptotic generalisation performance.
result Closed-form expression for generalisation performance in various high-dimensional settings.
RILA learns HQMMs robustly against adversarial corruption.
problem Robustness of HQMM learning algorithms under adversarial perturbations.
method Adversarially Corrupted HQMM (AC-HQMM) and Robust Iterative Learning Algorithm (RILA).
result RILA outperforms existing algorithms in convergence stability, corruption resilience, and physical validity.
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In particular, we introduce \emph{hidden physics models}, which are essentially data-efficien…
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
We present a machine learning framework for modeling protein dynamics. Our approach uses L1-regularized, reversible hidden Markov models to understand large protein datasets generated via molecular dynamics simulations. Our model is motivated by three design principles: (1) the requirement of massive scalability; (2) t…
Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.
problem No finite expression exists for Shannon entropy rates of hidden Markov processes.
method Developed an efficient method to calculate entropy rates and identify minimal predictive features.
result Entropy rates can be accurately calculated for hidden Markov processes.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
INO learns physical models with momentum conservation laws.
problem Learning physical models without preserving fundamental laws.
method Designing an invariant neural operator that automatically satisfies momentum conservation laws.
result The model learns complex material behaviors and achieves state-of-the-art accuracy and efficiency.
The hidden M-algebra is integrated into a super-Lie group, allowing for compactification of extra dimensions.
problem Integrating the hidden M-algebra into a super-Lie group to model super-exceptional spacetimes.
method Left-invariant extension of the decomposed M-theory 3-form, providing a computer-checked re-derivation and streamlined conception of super-Lie groups.
result Lattice subgroups of the hidden M-group allow toroidal compactification of hidden dimensions, akin to topological T-duality.
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations. In particular, we seek to leverage the underlying conservation laws (i.e., for mass, momentum, and energy) to infer hid…
This article proposes a method for mathematical modeling of human movements related to patient exercise episodes performed during physical therapy sessions by using artificial neural networks. The generative adversarial network structure is adopted, whereby a discriminative and a generative model are trained concurrent…
PIML enhances machine learning for subsurface energy systems.
problem Lack of interpretability and domain-specific knowledge in machine learning models.
method Integrates physics principles into data-driven models using deep learning.
result PIML improves model generalization and adherence to physical laws.
The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly non-linear statistical models, and just as linear models are amenable to linear a…
New method extracts hidden phases in binary mixtures using tubular tilings.
problem Hidden phases in binary mixtures are difficult to observe.
method Introduce tubular tilings for discretizing binary mixtures on smooth manifolds.
result Recover topological information about hidden phases from observable phases and interfaces.
Permutation of any two hidden units yields invariant properties in typical deep generative neural networks. This permutation symmetry plays an important role in understanding the computation performance of a broad class of neural networks with two or more hidden units. However, a theoretical study of the permutation sy…
DISTANA improves weather prediction by inferring hidden factors from temperature data.
problem Inferring hidden factors in spatiotemporal processes without supervision.
method Enhanced DISTANA architecture for spatiotemporal data, active tuning for latent state inference.
result DISTANA achieves more accurate predictions than other methods, inferring hidden factors from temperature data.
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.
Physics-informed neural networks struggle with stiffness leading to gradient imbalance.
problem Gradient pathologies in physics-informed neural networks.
method Learning rate annealing and novel neural network architecture.
result Significant improvement in predictive accuracy (50-100x) across various physics problems.
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as nonholonomic deformations of the Levi-Civita connection. Such deformations and induced…
New bandit algorithm maximizes information gain.
problem Optimizing decision-making in uncertain environments.
method Approximates information maximization using entropy and free energy principles.
result Asymptotic optimality proven for two-armed bandit problem.
Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities of interest. A different approach is to measure the quantities of interest and …
A scalable Bayesian additive model for stellar flare detection using Gaussian process inference and hidden Markov models.
problem Bayesian time-series modeling for astronomical datasets
method Generative surrogate framework with Variational Autoencoder and neural network forward pass
result Significant reduction in computational time for stellar flare detection
Benchmark tests LLMs on discovering physics laws in unconventional worlds.
problem Difficulties in distinguishing genuine reasoning from recall in LLMs across physics evaluations.
method Interactive benchmark with 22 worlds governed by various unconventional physics laws, requiring agents to design experiments and revise hypotheses.
result Strongest agents fail on worlds requiring latent structure discovery, highlighting limitations in long-term reasoning.
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field…
The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzi…
Framework infers conservation laws from trained neural networks.
problem Building reduced models of complex systems from physical data.
method Derives conservation laws from symmetries of dynamics in trained DNNs using Noether's theorem.
result Consistent results with previous studies for metastable collective motion systems.
Deep NURBS improves PINNs for solving PDEs on arbitrary geometries.
problem Solving partial differential equations on complex geometries with physics constraints.
method Combines admissible NURBS parametrizations and PINN solver for arbitrary geometries.
result High convergence rate and accuracy for most PDEs using Deep NURBS.
It is well established that neural networks with deep architectures perform better than shallow networks for many tasks in machine learning. In statistical physics, while there has been recent interest in representing physical data with generative modelling, the focus has been on shallow neural networks. A natural ques…
PINNs solve neuronal parameter and state estimation problems with limited data.
problem Estimating parameters and hidden state variables from noisy partial data in multiscale neuronal models.
method Physics-informed neural networks (PINNs) for joint state and parameter estimation.
result PINNs deliver robust and accurate parameter inference and state reconstruction, even with limited data.
Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent stru…
When encountering novel objects, humans are able to infer a wide range of physical properties such as mass, friction and deformability by interacting with them in a goal driven way. This process of active interaction is in the same spirit as a scientist performing experiments to discover hidden facts. Recent advances i…
Unified framework for analyzing neural networks in high dimensions.
problem Understanding neural networks' efficiency in high-dimensional data.
method Statistical physics techniques, including replica method and approximate message-passing algorithms.
result Unified analysis of various machine learning architectures and tasks.
Combines non-Euclidean and de Sitter geometries on the plane.
problem Exploring Penrose's Conformal Cyclic Cosmology.
method Geometric model combining Beltrami-Klein and de Sitter spaces.
result Discovery of hidden ${f G}_2$ symmetry in de Sitter spaces.
Study finds necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
problem Understanding the asymptotic behavior of black hole geometries.
method Used hidden symmetry and conformal geometry technology to find necessary conditions.
result Necessary conditions for black hole geometries to asymptotically approach Kerr-de Sitter spacetime.
NSIBF detects anomalies in CPS using neural system identification and Bayesian filtering.
problem Detecting anomalies in CPS with complex dynamics and sensor noise.
method Neural System Identification and Bayesian Filtering (NSIBF).
result NSIBF outperforms state-of-the-art methods in anomaly detection for CPS.
Bayesian Optimization tackles hidden constraints in architecture optimization.
problem Optimizing system architectures with hidden constraints using expensive physics-based simulations.
method Surrogate-based optimization with Gaussian Process models, including strategies for handling failed evaluations.
result Best performance achieved with a mixed-discrete GP predicting Probability of Viability (PoV) and minimum PoV threshold selection.
Physics-constrained deep learning predicts geophysical dynamics with boundedness.
problem Forecasting geophysical systems with hidden variables and incomplete observations.
method Physics-constrained neural ordinary differential equation (NODE) representations with boundedness constraints.
result The approach generalizes learned dynamics to arbitrary initial conditions.
This paper provides a tutorial on Boltzmann Machines and Deep Belief Networks.
problem Understanding and applying Boltzmann Machines and Deep Belief Networks.
method Explains the structures, conditional distributions, Gibbs sampling, training methods, and deep belief networks of RBMs.
result Comprehensive overview of RBMs and DBNs, useful in various fields.
Tensor-network techniques have enjoyed outstanding success in physics, and have recently attracted attention in machine learning, both as a tool for the formulation of new learning algorithms and for enhancing the mathematical understanding of existing methods. Inspired by these developments, and the natural correspond…
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.
A new neural network model identifies hysteresis universally.
problem Inability of existing models to simulate hysteresis universally.
method Inspired by the Preisach model, an Extended Preisach Neural Network (EPNN) is introduced with two hidden layers and a hybrid training algorithm.
result EPNN successfully identifies various hysteresis phenomena from different fields.
Generative AI predicts Arctic sea ice dynamics over decades.
problem Reproducing realistic sea ice dynamics from days to decades is computationally challenging.
method Introduced GenSIM, a generative AI model trained on 20 years of sea-ice-ocean simulation data.
result Generative AI predicts realistic sea ice evolution for 30 years, capturing long-term trends and physical consistency.
TNet combines DL with physics models to solve inverse problems efficiently.
problem Solving inverse problems with limited data and physics constraints.
method Model-constrained deep learning approach using TNet.
result TNet solutions are as accurate as traditional methods but faster.
FreB protocol uses AI to infer hidden parameters with valid confidence regions.
problem Generating biased or overconfident conclusions from AI-generated posterior distributions.
method Frequentist-Bayes (FreB) protocol reshapes AI-generated posterior distributions into valid confidence regions.
result FreB provides valid confidence regions that consistently include true parameters with expected probability.
Hydrodynamics principles applied to finance, solving complex market models.
problem Understanding financial market dynamics using physics principles.
method Unified mathematical framework using Kelvin waves to solve differential and pseudo-differential equations.
result Solved various financial models including volatility and variance swaps.