New algorithms tackle data challenges in physics model selection.
problem Lack of labeled data, high dimensionality, and inapplicability of data augmentation techniques to physics data.
method Two algorithms: feature selection and data augmentation combined with classifiers and stacking ensemble.
result Achieved 90% accuracy on nonlinear structural mechanics classification problem.
Bayesian framework calibrates imperfect models using physics-informed priors and Hamiltonian Monte Carlo.
problem Quantifying uncertainty in imperfect computer models described by differential equations.
method Physics-informed Gaussian process priors, discrepancy function, Hamiltonian Monte Carlo, data approximations.
result Framework accurately recovers true parameters and produces accurate predictions.
New GP model tackles physics constraints efficiently.
problem Lack of efficient, physics-informed models for complex systems.
method Physics-informed variational state-space Gaussian process.
result Efficient spatio-temporal modeling with improved performance.
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.
We find ways to make physical signals misclassified by computer vision models.
problem Vulnerability of signal classifiers to adversarial perturbations in physical signals.
method Solving PDE-constrained optimization problems to construct imperceptible perturbations.
result Effective and physically realizable adversarial perturbations can be computed for machine learning models.
Anomaly Awareness detects anomalies in particle physics and computer vision.
problem Detect anomalies in complex data sets.
method Modifies cost function to learn normal events and anomalies.
result Effective at identifying new anomalies not previously seen.
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.
New sampling scheme improves ML accuracy in physics simulations.
problem Improving accuracy of ML models in physics simulations.
method Taylor-based data sampling scheme for DNNs.
result Reduces error in DNN solutions of ODE systems.
Restricted Boltzmann machines (RBMs) are powerful machine learning models, but learning and some kinds of inference in the model require sampling-based approximations, which, in classical digital computers, are implemented using expensive MCMC. Physical computation offers the opportunity to reduce the cost of sampling …
Interpretable meta-learning for physical systems reduces computational costs and improves interpretability.
problem Challenges in learning from heterogeneous experimental data.
method Affine structure learning model for multi-environment generalization.
result Proves the model can identify physical parameters and demonstrates competitive performance.
The paper extends IPC framework to stationary physical systems and validates it with a photonic system.
problem Characterizing the computational capabilities of stationary physical systems in a principled, data-efficient way.
method Extended IPC framework, established fundamental results, derived asymptotic bias, introduced data-efficient estimation methods.
result IPC strongly correlates with machine-learning performance and provides a reliable estimate of system dimensionality.
This work integrates differentiation and integration in Physics-Informed Neural Networks.
problem Solving integro-differential equations and computing integral transforms.
method Augmenting Physics-Informed Neural Networks with automatic integration.
result Solving complex integral transforms and integro-differential equations.
Steerable E(3) Graph Neural Networks incorporate geometric and physical covariant information.
problem Incorporating covariant information like position, force, velocity, or spin in graph neural networks.
method Steerable E(3) Equivariant Graph Neural Networks (SEGNNs) that use steerable MLPs to incorporate geometric and physical covariant information.
result SEGNNs improve upon classic linear point convolutions and recent equivariant graph networks that send invariant messages.
Paper explores physics-informed deep learning for system reliability assessment.
problem Limited study on deep learning for system reliability assessment.
method Physics-informed deep learning approach for system reliability assessment.
result Physics-informed deep learning can alleviate computational challenges and combine measurement data and mathematical models.
This chapter reviews classic regression methods and their evolution to physics-informed approaches.
problem Finding relationships between variables using regression.
method Introduces traditional and physics-informed regression methods, linking them to computational science.
result Regression methods have evolved from purely statistical to incorporating physical knowledge.
LOT framework speeds up event distance computation in collider physics.
problem Computational inefficiency in quantifying event distances.
method Linearized Optimal Transport (LOT) for efficient computation.
result LOT significantly reduces computational cost without sacrificing accuracy.
High-precision machine learning reduces particle physics simulations by orders of magnitude.
problem Reducing computational burden in particle physics simulations.
method Developed optimal training strategies and tuned machine learning regressors, including Deep Neural Networks with skip connections and boosted decision trees.
result Significantly reduced computational time by factors of 10^3 to 10^6 over first-principles simulations.
An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by Partial Differential Equation (PDE), and its loading/ response mapping can be solve…
The issue of computing (co)homology generators of a cell complex is gaining a pivotal role in various branches of science. While this issue can be rigorously solved in polynomial time, it is still overly demanding for large scale problems. Drawing inspiration from low-frequency electrodynamics, this paper presents a ph…
The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.
problem Computing volumes for physical gravity models.
method Topological recursion and physical two-dimensional gravity models.
result Derivation of Virasoro constraints and cut-and-join equations for generalized Mirzakhani's recursions.
Physics-informed kernel learning integrates physical priors into machine learning models.
problem Tackles the integration of physical laws into machine learning models for improved accuracy and efficiency.
method Uses Fourier methods to approximate the kernel and minimizes a physics-informed risk function.
result Demonstrates PIKL outperforms physics-informed neural networks and traditional PDE solvers in various scenarios.
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…
EFiGP uses Fourier and eigen-decomposition for efficient ODE parameter estimation.
problem Parameter estimation and trajectory reconstruction for noisy, sparse, nonlinear ODE systems.
method EFiGP integrates Fourier transformation and eigen-decomposition into a physics-informed Gaussian Process framework.
result EFiGP efficiently estimates ODE parameters and recovers trajectories from noisy data.
New algorithms improve vascular flow simulations in aortic aneurysms.
problem Limited accuracy of MRI in hemodynamics, patient-specific flow boundary conditions, and CFD's computational demands.
method Physics-Informed Neural Networks (PINNs) and Deep Operator Networks (DeepONets) integrated with 3D Navier-Stokes equations.
result Improved computational efficiency and good agreement with CFD simulations.
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.
Transformers predict scattering amplitudes in theoretical physics.
problem Computing exact coefficients of scattering amplitudes in N = 4 SYM theory.
method Applied Transformers to predict integer coefficients of scattering amplitudes.
result Transformers achieve high (> 98%) accuracy on predicting scattering amplitudes.
New method uses EKI for efficient Bayesian inference in high-dimensional problems.
problem Efficient inference for high-dimensional posterior distributions in physics-informed neural networks.
method Ensemble Kalman Inversion (EKI) for high-dimensional posterior inference.
result EKI-based inference provides comparable uncertainty estimates to HMC-based methods but with reduced computational cost.
Machine learning accelerates Lie algebra computations.
problem Computing tensor products and branching rules of Lie algebras.
method Machine learning for Lie algebra computations.
result Achieves significant speed-ups in Lie algebra computations.
This work discovers governing equations from limited data using physics-informed deep learning.
problem Discovering governing equations from scarce and noisy data for complex systems.
method Physics-informed deep learning framework integrating neural networks, physics embedding, and sparse regression.
result The method effectively identifies governing equations from various spatiotemporal systems with different levels of data scarcity and noise.
Enhanced PC2 improves surrogate modeling for high-dimensional problems.
problem Degrading performance and efficiency of PC2 in high-dimensional parameter spaces. method Integrates SULM solver and D-optimal sampling strategy into PC2 framework. result Enhanced PC2 demonstrates better comprehensive capability and efficiency. New methods link Calabi-Yau metrics to random matrices.
problem Lack of explicit metrics on Calabi-Yau manifolds hinders particle physics computations.
method Numerical approximations of the Laplacian spectrum on Calabi-Yau spaces.
result Surprising link found between Calabi-Yau metrics and random matrix theory.
Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparat…
PILNO uses neural operators to solve PDEs efficiently on point clouds.
problem Solving partial differential equations (PDEs) on point cloud data efficiently.
method Physics-informed low-rank neural operator framework combining low-rank kernel approximations and an encoder-decoder architecture.
result PILNO efficiently approximates solution operators of PDEs on point cloud data, satisfying PDE constraints and boundary conditions.
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.
Machine learning improves combustion system predictions by integrating physical models.
problem Improving accuracy of complex multi-physics systems like combustion.
method Coupling machine learning algorithms with physical models and constraints.
result Enhanced predictive capabilities in turbulent combustion.
A new method learns physical system sensitivity to improve policy learning without needing a full model.
problem Expensive policy learning without models and model bias.
method Learn sensitivity of trajectories to parameter perturbations.
result Feasibility demonstrated on a physical robot.
Neural model predicts object states and physical parameters from visual observations.
problem Computational models struggle with physical reasoning and adapting to new environments.
method Visual prior predicts particle-based system from visual observations; inference module refines estimates subject to dynamics constraints.
result Model can infer physical properties within a few observations and adapt to unseen scenarios.
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
This work combines machine learning with physical models to solve inverse problems efficiently.
problem Solving inverse problems in the presence of missing physics and recovering parameters.
method Variational autoencoding with a physically structured decoder network and stochastic local approximations.
result The method accelerates inference for Bayesian inverse problems and acts as a regularizer encoding prior physical information.
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.
New method uses PINNs to efficiently compute Gerber-Shiu functions.
problem Calculating the Gerber-Shiu function efficiently.
method Physics-informed neural networks (PINNs) embedded with differential equations.
result Demonstrates good performance in approximating Gerber-Shiu functions.
Develops scalable differentiable physics for complex object interactions.
problem Limited scalability of existing differentiable physics solvers.
method Adopting meshes for arbitrary geometry, localized collision handling, and accelerated implicit differentiation.
result Significantly reduces memory and computation requirements compared to particle-based methods.
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems. These are regimes in which the underlying statistical problem is information-theoretically possible although no efficient algorithm exists, rendering the problem essentially unsolvable for large instances…
New method identifies physical constants from video data alone.
problem Identifying physical constants from video data.
method Proves level-set slope-coverage condition ensures local affine mapping to true physical state, enabling exact parameter recovery.
result Underdamped systems identifiable from a single video clip, other regimes require three diverse trajectories.
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…
Physics-informed deep learning approximates strain gradient plasticity solutions.
problem Stiffness and computational challenges in solving strain gradient plasticity models.
method Physics-informed deep learning (PIDL) with modified loss functions and optimization schemes.
result PIDL methods address stiffness and computational challenges in strain gradient plasticity.
New trends explore quantum machine learning to speed up computations and analyze data.
problem Speeding up machine learning computations and analyzing large quantum data.
method Interplay between quantum physics and machine learning, including new algorithms and hardware.
result Breakthroughs in quantum machine learning can provide advantages over classical methods.
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.