Study permeable sets and their dimensions, with applications to fractals.
problem Understanding permeability and dimensions of sets.
method Investigate permeable sets and their properties, establish theorems on permeability and dimension relations.
result Most subsets of \(\mathbb{R}^d\) with dimension less than \(d-1\) are permeable.
A machine learning method predicts rock permeability from 3D images.
problem Efficiently predict permeability of heterogeneous rocks for planetary and robotic applications.
method Machine learning guided 3D properties recognition of rock morphology from 3D micro CT and MRI images.
result The morphology decoder method accurately predicts permeability from 3D images.
Generative adversarial networks improve geological model generation.
problem Capturing complex geological structures in subsurface models.
method Wasserstein GAN for parametrization and generation of geological models.
result GANs preserve multipoint statistical features of geological models.
CNNs predict porosity, permeability, and tortuosity from porous media images.
problem Predicting key properties of porous media from images.
method Convolutional neural networks (CNNs) trained with lattice Boltzmann simulations.
result CNNs accurately predict porosity, permeability, and tortuosity.
Research shows Twitter is permeable to financial events, influencing its content and sentiment.
problem Investigating how Twitter reacts to financial events.
method Conducted experiments on a specific financial event (Tesco PLC and Booker Group PLC merger announcement).
result Twitter is permeable to financial events, affecting its content and sentiment.
Machine learning predicts rock properties from routine core analysis.
problem Predict rock properties like porosity and permeability from routine core analysis.
method Developed and compared machine learning models (NN, SVM, LR).
result Neural network with hidden layers best for all rock properties.
Develops a data-driven model for porous media flow simulations.
problem Capturing flow field and permeability in digital porous media.
method Data-driven approach using Lattice Boltzmann simulation data.
result Accurately predicts flow solutions with reduced computational time.
Generative adversarial networks improve stochastic input parametrization in subsurface flow simulations.
problem Effective parametrization of high-dimensional, correlated stochastic inputs in subsurface flow simulations.
method Training a generative adversarial network to emulate the data generating process of stochastic inputs.
result Generative adversarial networks preserve both visual realism and high-order statistics of flow responses, achieving a significant dimensionality reduction.
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
ROMs predict thermal power output in EGS systems, accounting for uncertainties.
problem Predicting transient thermal power output in enhanced geothermal systems (EGS) with subsurface uncertainties.
method Developed regression-based ROMs using physics-based simulations and Latin Hypercube Sampling.
result Three ROMs (1, 2, 3) accurately describe power production curves, with ROM-2 and ROM-3 outperforming ROM-1 for typical EGS applications.
Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.
problem Accurate simulation of fluid flow in complex porous media requires excessive computational resources.
method Combining deep learning with direct simulation, using Gated U-Net CNNs trained on datasets of 2D and 3D porous media.
result Deep learning predictions can reach over 90% accuracy for permeability estimation and accelerate simulations by orders of magnitude.
A new method for solving complex inverse problems using deep learning.
problem Estimating complex spatially-varying parameters in high-dimensional Bayesian inverse problems.
method A variational inference method with a deep generative prior to approximate the posterior distribution.
result The method improves estimation accuracy and efficiency for solving high-dimensional inverse problems.
Deep neural network predicts multiphase flow in heterogeneous domains.
problem Predicting multiphase flow in complex, heterogeneous systems.
method Deep neural network model for handling permeability heterogeneity and learning interplay of forces.
result Highly accurate predictions of CO2 saturation distribution with computational efficiency.
Bayesian model tackles high-dimensional inverse problems efficiently.
problem Estimating spatially-varying parameters in expensive models.
method Multiscale Bayesian inference with deep generative models and MCMC.
result Efficient estimation of global and local parameter features.
Unified framework for Bayesian PDE-constrained inversion using physics-informed neural networks.
problem Incorporating prior distributions in function space into Bayesian PINN-based inversion.
method Functional-prior-based approaches (fpBPINN) to Bayesian PDE-constrained inversion using physics-informed neural networks (PINNs). Two complementary approaches: FPI-BPINN and fParVI-PINN.
result Accurate estimation of posterior distributions in seismic traveltime tomography and Darcy-flow permeability inversion.
Deep neural network models for efficient uncertainty quantification in multiphase flow.
problem Uncertainty quantification of dynamic multiphase flow in heterogeneous media due to high dimensionality and discontinuities.
method Convolutional encoder-decoder neural network for image-to-image regression, incorporating time as an input.
result Accurate surrogate model capable of characterizing spatio-temporal pressure and saturation fields with limited training data.
Bayesian CNNs improve surrogate modeling and uncertainty quantification for stochastic PDEs.
problem Uncertainty quantification and propagation in stochastic PDEs.
method Bayesian deep convolutional encoder-decoder networks with Stein's gradient descent.
result Achieves state-of-the-art predictive accuracy and uncertainty quantification.
A neural network predicts coarse-scale basis functions for efficient uncertainty quantification.
problem Efficiently estimating coarse-scale basis functions for multiscale methods.
method Data-driven approach using neural networks fitted to solution samples.
result Significant computational savings for uncertainty quantification tasks.
VAE improves MCMC efficiency by generating diverse prior proposals.
problem Inefficient MCMC methods in Bayesian inverse problems, especially subsurface flow modeling.
method Uses Variational Autoencoder (VAE) to generate broader-spectrum prior proposals.
result VAE achieves comparable accuracy to Karhunen-Loève Expansion (KLE) and outperforms it when correlation length is unknown.
Experimental design is crucial for inference where limitations in the data collection procedure are present due to cost or other restrictions. Optimal experimental designs determine parameters that in some appropriate sense make the data the most informative possible. In a Bayesian setting this is translated to updatin…
Generative adversarial networks reconstruct oolitic limestone micro-structures.
problem Stochastic image reconstruction of oolitic limestone micro-structures.
method Generative adversarial neural networks (GANs) for unsupervised learning.
result GANs accurately reconstruct oolitic limestone micro-structures.
New concepts of barriers and black regions defined for Lorentzian manifolds.
problem Understanding causal world-lines and horizons in Lorentzian manifolds.
method Proving properties of null hypersurfaces and their causal world-lines.
result Null hypersurfaces are semi-permeable, leading to new concepts of barriers and black regions.
Deep learning speeds up pressure prediction in carbon storage reservoirs.
problem Accurately forecasting reservoir pressure in geologic carbon storage projects with sparse well data.
method Combining InSAR surface displacement data with deep learning and data assimilation techniques.
result Workflow can predict reservoir pressure with high efficiency and uncertainty quantification.
The paper extends algebraic expression for subjective spatial patterns to include temporal patterns.
problem Studying subjective spatial and temporal patterns in machine learning.
method Develops X-form for algebraic expression of subjective spatial patterns and extends it to temporal patterns.
result Established algebraic expressions for both spatial and temporal patterns.
Safe Pattern Pruning reduces pattern explosion in predictive pattern mining.
problem Exponential growth of patterns in structured data.
method Safe Pattern Pruning (SPP) method.
result Effective model building in practical data analysis.
Developed MF-PINNs to solve coupled Stokes-Darcy equations more accurately.
problem Solving coupled Stokes-Darcy equations with varying physical constants.
method Combining VP and SV forms with adjusted weights in MF-PINNs.
result Improved accuracy of streamline and pressure fields in numerical experiments.
This study recovers electromagnetic parameters on boundaries from impedance and admittance data.
problem Recovering anisotropic electromagnetic parameters from boundary impedance and admittance data.
method Formulated inverse boundary value problem for time-harmonic Maxwell's equations on differential 1-forms.
result Knowledge of impedance and admittance maps determines tangential entries of induced metrics at the boundary.
BN^2MF identifies unknown exposure patterns in environmental mixtures.
problem Identifying unknown exposure patterns in environmental mixtures.
method Bayesian non-parametric non-negative matrix factorization (BN^2MF) with non-negative continuous priors and a non-parametric sparse prior.
result Estimates patterns of chemical exposures without specifying the number of patterns.
RestoreAI predicts landmine risk from patterns, improving clearance efficiency.
problem Predicting landmine risk from spatial patterns to enhance clearance efficiency.
method RestoreAI uses landmine patterns for risk prediction, implementing three deminers: linear, curved, and Bayesian.
result RestoreAI significantly boosts clearance efficiency, achieving a 14.37 percentage point increase in cleared landmines per timestep.
Study of knots with generalized Mazur patterns and their invariants.
problem Understanding the invariants and properties of knots with generalized Mazur patterns.
method Computational analysis of τ and ε invariants for n-twisted satellites. result None of the n-twisted patterns from the family act surjectively on the smooth or rational concordance group. Safe pattern pruning finds predictive patterns efficiently.
problem Finding optimal predictive patterns in databases.
method Safe Pattern Pruning (SPP) method for predictive pattern mining.
result SPP method efficiently finds superset of all needed predictive patterns.
Paper proves rigidity of spherical ring patterns on surfaces.
problem Proving rigidity of spherical orthogonal ring patterns on closed surfaces.
method Modification of combinatorial total geodesic curvature and variational principles.
result Rigidity of spherical orthogonal ring patterns on closed surfaces proved.
Two approaches detect EV charging patterns at stations.
problem Identify charging patterns at electric vehicle charging stations.
method Two approaches: rule-based and hierarchical clustering.
result Hierarchical clustering revealed unexpected charging patterns.
Proves existence of circle patterns on surfaces with cusps.
problem Existence of circle patterns with prescribed angles on surfaces with cusps.
method Introduced combinatorial Ricci and Calabi flows to prove longtime existence and convergence.
result Existence of generalized circle patterns with prescribed angles on surfaces with cusps.
Study of combinatorial Calabi flow on ideal circle patterns.
problem Finding ideal circle patterns with prescribed curvatures.
method Combinatorial Calabi flow in hyperbolic and Euclidean geometry.
result Flow converges exponentially to ideal circle patterns.
The paper studies circle patterns on surfaces with specific angles and curvature maps.
problem Investigating circle patterns with obtuse angles on surfaces of finite type.
method Characterizing curvature maps and establishing combinatorial Ricci flow conditions.
result Generalizations of circle pattern theorem and a computational method to find patterns.
Flexics samples patterns with guarantees, addressing flexibility and accuracy issues.
problem Pattern explosion and limited sampling accuracy with existing methods.
method Leverages SAT sampling and pattern mining algorithms to support flexible quality measures and constraints.
result Flexics provides strong guarantees on sampling accuracy while being flexible and efficient.
The paper extends circle pattern theory to include obtuse angles.
problem Existence and rigidity of circle patterns with non-obtuse exterior intersection angles.
method Topological degree theory, variational principle, Teichmüller theory, Sard's Theorem.
result The Circle Pattern Theorem is generalized to include obtuse angles.
CDPA identifies common and distinctive patterns in high-dimensional datasets.
problem Existing methods fail to capture the common pattern between coefficient matrices of shared latent factors.
method Proposes CDPA, an unsupervised learning method that incorporates both common and distinctive patterns of coefficient matrices.
result CDPA provides better characterization of common and distinctive patterns in high-dimensional datasets.
Study circle patterns on tori, linking symplectic forms and homeomorphisms.
problem Understanding circle patterns on tori and their symplectic properties.
method Investigates the space of circle patterns on closed tori with complex projective structures, embedding it into Teichmüller spaces and analyzing symplectic forms.
result Non-degeneracy of the pulled-back Weil-Petersson symplectic form and homeomorphism between circle patterns and Teichmüller spaces.
FSR efficiently discovers significant patterns with few resampled datasets.
problem Mining significant patterns in transactional data, especially subgroups.
method FSR uses resampling to bound the supremum deviation of quality statistics, providing rigorous guarantees on false discoveries.
result FSR effectively discovers significant subgroups with a small number of resampled datasets.
Study uses CNN and LSTM to recognize stock chart patterns.
problem Recognizing stock chart patterns for trading.
method Used CNN and LSTM neural networks on historical stock data.
result Obtained accuracies for recognizing two common chart patterns.
Discovers discriminative patterns in two-class datasets.
problem Discovering patterns that occur more frequently in one class than the other.
method Proposes SSDPS algorithm with an original enumeration strategy exploiting anti-monotonicity.
result SSDPS outperforms other algorithms in terms of efficiency and pattern generation.
Method computes pattern time statistics from random sequences.
problem Extracting temporal regularities from random sequences.
method Using generating functions for Markov and Bernoulli trials.
result Pattern time statistics cover various measurements in learning.
TFPS improves time series forecasting by learning pattern-specific experts.
problem Challenges in forecasting time series data with varying patterns across segments.
method Dual-domain encoder, subspace clustering, pattern-specific experts.
result Significantly improved forecasting accuracy, especially in long-term forecasting.
Paper discovers shifting patterns in sequence classification and proposes a method to improve performance.
problem Discriminative patterns in sequential data are time-dependent and degrade traditional classification methods.
method Proposes a novel sequence classification method using multi-instance learning and LSTM models to detect and model shifting patterns.
result Demonstrates superior sequence classification performance and detection of shifting patterns in cropland mapping and affective state recognition.
The paper integrates statistical significance and discriminative power in pattern discovery.
problem Discovering actionable patterns that meet rigorous statistical significance and discriminative power criteria.
method Integrates statistical significance and discriminative power criteria into state-of-the-art algorithms.
result Improves discriminative power and statistical significance of discovered patterns without quality deterioration.
Generative model attacks CNN on MNIST by subtly replacing input patterns.
problem Adversarial attacks on neural networks.
method Generative model that replaces input patterns with generated ones.
result Demonstrated effectiveness on MNIST dataset.