Efficient surrogate modeling for complex PDEs with physical laws.
problem High computational cost of repeated PDE simulations.
method LC-prior Gaussian process with POD and RBF-FD.
result Significantly reduced computational cost and improved accuracy.
New method combines machine learning with data assimilation for model error correction.
problem Correcting model errors using sparse and noisy observations.
method Hybrid machine learning and data assimilation methods.
result Tendency correction outperforms resolvent correction in data assimilation experiments.
Paper addresses hypothesis space misspecification in learning from human demonstrations and corrections.
problem Hypothesis space misspecification in learning from human demonstrations and corrections.
method Reason explicitly about how well the robot can explain human inputs given its hypothesis space.
result Demonstrates method on a 7 DOF robot manipulator.
Sig-PCA integrates model outputs and observations to correct model biases.
problem Improving model accuracy and reliability by correcting biases and numerical approximations.
method Sig-PCA framework that combines summary statistics from model outputs with localized observations via a neural network.
result Corrects model outputs to align closely with observational data, preserving essential statistical information.
Bayesian hybrid models correct for missing physics in machine learning.
problem Systematic bias in machine learning models.
method Fusing physics-based insights with machine learning constructs, using Bayesian calibration and stochastic programming.
result Bayesian hybrid models outperform pure machine learning approaches with less data.
We investigate a statistical-static hedging technique for pricing assets considered as single-step stochastic cash flows. The valuation is based on constructing in a canonical way a European style derivative on a benchmark security such that the physical payoff distribution coincides with the (corrected) physical asset…
System predicts ice formation to improve road safety.
problem Improving road safety through accurate ice formation prediction.
method Combining physical models and machine learning for data correction.
result Machine learning effectively corrects incorrect data in forecasts.
New method preserves GCM spatial dependencies for better climate projections.
problem Systemic biases in GCM output and loss of spatial/temporal dependencies.
method SPECD approach using Vecchia approximation and semi-parametric quantile regression.
result SPECD preserves key marginal and joint distribution properties of precipitation and temperature.
We study the physics of globally consistent four-dimensional N=1 supersymmetric M-theory compactifications on G2 manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits U(1)3 gauge symmetry and a spectrum o…
Reweighting improves GAN accuracy without sacrificing statistical power.
problem Improving the fidelity of generative models.
method Post-hoc reweighting function applied to generated examples.
result Weighted GAN examples significantly improve accuracy.
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
problem Training instability and reduced accuracy in PINNs for complex PDEs.
method Adaptive curvature correction using secant information to optimize first-order optimizers.
result Consistent improvements in convergence speed, stability, and accuracy over standard optimizers.
Machine learning in context of physical systems merits a re-examination of the learning strategy. In addition to data, one can leverage a vast library of physical prior models (e.g. kinematics, fluid flow, etc) to perform more robust inference. The nascent sub-field of \emph{physics-based learning} (PBL) studies the bl…
Improved variational inference for geophysical inverse problems with data correction.
problem High computational cost and accuracy issues in Bayesian inference for geophysical inverse problems.
method Amortized variational inference with latent distribution correction using physics-based priors.
result Improved robustness of amortized variational inference under data distribution shifts.
Study loop corrections in random feature models affecting training and test errors.
problem Analyzing loop corrections in random feature models to understand training and test errors.
method Statistical physics and effective field theory approach to study loop corrections.
result Derived loop corrections to training error, test error, and generalization gap.
This paper explores formal verification for autonomous systems, identifying limitations and proposing improvements.
problem Ensuring safety of autonomous systems like self-driving cars and drones.
method Formal verification techniques based on formal methods, analyzing three assumptions and their limitations.
result Preliminary work to improve the strength of evidence provided by formal verification.
Improved PINNs for solving PDEs with unknown measurement noise.
problem Handling non-Gaussian noise in physics-informed neural networks.
method Jointly train an EBM to learn the correct noise distribution.
result Improved performance in solving PDEs with non-Gaussian noise.
Machine-learned anomaly detection in new-physics searches needs calibration and look-elsewhere correction
problem Machine-learned anomaly detection in new-physics searches
method Conformal prediction layer
result Calibrated significance with distribution-free guarantees
In this comment on "Solving Statistical Mechanics Using Variational Autoregressive Networks" by Wu et al., we propose a subtle yet powerful modification of their approach. We show that the inherent sampling error of their method can be corrected by using neural network-based MCMC or importance sampling which leads to a…
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.
Estimates reliability of nuclear fuel using advanced modeling techniques.
problem Determining the reliability of TRISO-coated particle fuel, which has small failure probabilities and expensive computational models.
method Coupled active learning, multifidelity modeling, and subset simulation.
result Multifidelity modeling strategies consistently reduce the number of high-fidelity model calls.
Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when …
Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models still show many differences compared with observations. Machine learning has bee…
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.
We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.
Physen-Noise2Noise tackles defocus deblurring in low-light conditions with physics-guided self-supervised learning.
problem Defocus deblurring in low-light conditions with complex biased noise.
method Physics-guided self-supervised deblurring framework that leverages noisy multi-frame observations and a learnable noise bias parameter.
result Physen-Noise2Noise consistently outperforms state-of-the-art methods in defocus deblurring with complex biased noise.
SCaSML improves PDE solvers by correcting errors efficiently.
problem Reliable and error-free high-dimensional PDE solutions.
method Defect correction method to derive a Structural-preserving Law of Defect.
result SCaSML achieves faster convergence and reduced errors in high-dimensional PDEs.
The paper uses optimal transport to calibrate stochastic simulations.
problem Improper fidelity of stochastic simulators in scientific applications.
method Optimal transport theory applied to neural network corrections.
result Calibrated stochastic simulations improve fidelity to reality.
Mathematical study of instanton corrected q-map spaces and their isometries.
problem Understanding the isometries of instanton corrected q-map spaces.
method Study of isometries of instanton corrected q-map spaces associated to PSR manifolds.
result Explicit example of instanton corrected q-map space with full SL(2,Z) acting by isometries.
In this note, we study the SYZ mirror construction for a toric Calabi-Yau manifold using instanton corrections coming from Woodward's quasimap Floer theory instead of Fukaya-Oh-Ohta-Ono's Lagrangian Floer theory. We show that the resulting SYZ mirror coincides with the one written down via physical means (as expected).
Improved model error correction online with neural networks in 4D-Var.
problem Reconstructing dynamics of imperfectly observed physical models.
method Weak-constraint 4D-Var framework with online neural network training.
result Online model error correction yields more accurate results than offline.
Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of…
Learning robot objective functions from human input has become increasingly important, but state-of-the-art techniques assume that the human's desired objective lies within the robot's hypothesis space. When this is not true, even methods that keep track of uncertainty over the objective fail because they reason about …
Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.
problem Construct quaternionic-Kähler metrics from special Kähler manifolds with mutually local variations of BPS structures.
method Construct quaternionic-Kähler metrics from a conical special Kähler manifold with a certain type of mutually-local variation of BPS structures. Provide global and local explicit formulas for the quaternionic-Kähler metric.
result Construct quaternionic-Kähler metrics that are positive-definite and deform the 1-loop corrected Ferrara-Sabharval metric.
Deep learning improves low-fidelity dynamical models with scarce high-fidelity data.
problem Improving low-fidelity models with limited high-fidelity data.
method Transfer learning using a deep neural network to correct a low-fidelity model.
result An improved DNN model with high accuracy to underlying dynamics.
Modeling wildfire aerosols using satellite data to predict solar radiation reduction.
problem Accurately estimate and predict AOD propagation from wildfires using multi-source satellite data.
method Physics-informed statistical modeling integrating multi-source satellite data with an advection-diffusion equation.
result The proposed approach accurately predicts AOD propagation and demonstrates model interpretability.
New method for unbinned, profiled unfolding in particle physics.
problem Traditional unfolding methods are limited in the number of unfolded variables and cannot profile nuisance parameters.
method Proposes a machine learning-based method that allows for unbinned differential cross sections and profiles nuisance parameters.
result Demonstrates the method with Gaussian examples and a simulated Higgs boson cross section measurement.
Paper stabilizes generative model training with synthetic data.
problem Self-consuming loops in generative model training.
method Introducing an idealized correction function and self-correction functions.
result Self-consuming loops can be exponentially more stable with the right correction.
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse accurate observation data are available. Specifically, the two types of multifi…
The paper develops methods to assess and correct model uncertainties in graphical models.
problem Model uncertainty in probabilistic graphical models.
method Information-theoretic and non-parametric stress tests.
result Ranking and correcting impactful sources of uncertainty in graphical models.
A new machine learning method handles nuisance parameters for better unfolding in particle physics.
problem Improving statistical correction of cross sections in complex particle physics detectors.
method Profile OmniFold, a machine learning-based Expectation-Maximization procedure that incorporates nuisance parameters.
result Demonstrated the effectiveness of Profile OmniFold on both simulated and real data.
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
problem Understanding the principles behind emergent intelligent behaviors in disordered systems.
method Statistical physics approach to charting learning mechanisms and dynamics.
result Uncovering relationships between learning mechanisms and physical dynamics.
Mathematical models are used extensively for diverse tasks including analysis, optimization, and decision making. Frequently, those models are principled but imperfect representations of reality. This is either due to incomplete physical description of the underlying phenomenon (simplified governing equations, defectiv…
PINNs struggle with increasingly complex ODEs, especially when parameters control their complexity.
problem Evaluating physics-informed neural networks on complex coupled ODEs.
method Tuned benchmarks of partial differential equations and harmonic oscillators; varying network architecture and training method.
result PINNs fail to solve complex ODEs, revealing issues like insufficient capacity, poor conditioning, and high local curvature.
Deep Reinforcement Learning (DRL) has become a powerful strategy to solve complex decision making problems based on Deep Neural Networks (DNNs). However, it is highly data demanding, so unfeasible in physical systems for most applications. In this work, we approach an alternative Interactive Machine Learning (IML) stra…
New ML methods improve physical system understanding by quantifying uncertainty across diverse regimes.
problem Capturing multi-regime physical systems with standard ML techniques.
method Coverage-oriented uncertainty quantification (UQ) methods.
result Coverage-oriented UQ models deliver physically consistent uncertainty estimates.
Neural CDEs correct errors in learned time-series models for better forecasting.
problem Error accumulation in multi-step forecasts of learned time-series models.
method Predictor-Corrector framework with a neural controlled differential equation.
result The proposed framework consistently improves forecasting performance across various models.
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.
We introduce a new high dimensional algorithm for efficiency corrected, maximally Monte Carlo event generator independent fiducial measurements at the LHC and beyond. The approach is driven probabilistically using a Deep Neural Network on an event-by-event basis, trained using detector simulation and even only pure pha…