Machine learning reduces DFN size by 80% for faster simulations.
problem Simulating flow and transport in large DFNs is computationally intensive.
method Graph theory and machine learning to identify a smaller, representative network.
result Reduced network size by approximately 20% without losing breakthrough curves.
This paper analyzes uncertainty in DFN simulations using sensitivity analysis.
problem Uncertainty in estimating QoI due to epistemic and aleatoric uncertainties in DFN simulations.
method Sensitivity analysis to attribute uncertainty to input parameters and aleatoric uncertainty.
result Characterizes uncertainty in DFN flow simulations with heteroskedastic aleatoric uncertainty.
Generalized meshes for non-regular geometries, including fractures.
problem Discretization of partial differential equations in non-regular geometries.
method Introduces generalized meshes with overlapping elements and flexible adjacency relations.
result Discrete differential forms on virtually inflated meshes characterize the trace space of forms in surrounding volumes.
Subsurface applications including geothermal, geological carbon sequestration, oil and gas, etc., typically involve maximizing either the extraction of energy or the storage of fluids. Characterizing the subsurface is extremely complex due to heterogeneity and anisotropy. Due to this complexity, there are uncertainties…
Predicts fracture evolution and material failure in brittle materials.
problem Predicting how fractures propagate and materials fail in brittle materials.
method Recurrent graph convolutional neural networks trained on simulation data.
result Predictions within 3% for fracture damage and 15% for time to failure.
Deep learning system detects hip fractures as well as radiologists.
problem Automatically identifying hip fractures from x-rays.
method Trained on 53,000 clinical x-rays, system achieves 0.994 ROC curve.
result Equivalent diagnostic performance to human radiologists.
Study models fractures in porous media using geometric analysis.
problem Analyzing fluid flow in fractures with complex geometries.
method Developed a geometric model using Riemannian manifold and Laplace Beltrami operators.
result Reduced model accurately approximates flow in complex fractures.
Paper presents ML approaches for faster brittle fracture modeling.
problem Faster modeling of brittle fracture in concrete.
method Machine learning algorithms combined with physics-based assumptions.
result ML models are orders of magnitude faster than high-fidelity models.
Enhanced PINN for brittle fracture modeling using transfer learning.
problem Solving brittle fracture problems in physics.
method Physics-informed neural network (PINN) with variational energy minimization and transfer learning.
result The proposed approach yields better accuracy in predicting crack paths compared to conventional PINN.
Efficient deep learning model classifies fractures from X-rays.
problem Manual X-ray examination of fractures is time-consuming and error-prone.
method Robust training loop using transfer learning and latest dataset.
result Model achieves superior performance in less than ten epochs.
The paper uses ML to predict oil rate post-HF, comparing it to engineers' predictions.
problem Predicting oil rate post-hydraulic fracturing.
method Data-driven model using ML techniques on fracturing job data.
result ML predictions outperform engineers' predictions.
Optimizes structure topology for ductile and brittle fracture resistance.
problem Minimizing mass while ensuring structural damage and fracture resistance.
method Phase-field approach for modeling fracture, level-set topology optimization.
result Enhanced fracture resistance through two formulations.
Fractured Sampling improves LLM reasoning efficiency by truncating CoT trajectories.
problem Efficiently scaling reasoning in large language models with limited tokens.
method Integrating truncated Chain-of-Thought (CoT) with Fractured Sampling across multiple dimensions.
result Fractured Sampling achieves superior accuracy-cost trade-offs compared to full CoT.
We use topological methods to prove a semicontinuity property of the Hodge spectra for analytic germs defined on an isolated surface singularity. For this we introduce an analogue of the Seifert matrix (the fractured Seifert matrix), and of the Levine--Tristram signatures associated with it, defined for null-homologous…
Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.
problem Coupling multiphysics simulations on graphs with conservation constraints.
method Gaussian processes combined with discrete exterior calculus and maximum likelihood estimation.
result Data-driven predictions with uncertainty quantification on entire graph.
Optimal design portfolios improve energy efficiency and reduce risk in uncertain reservoirs.
problem Uncertain reservoir conditions lead to unstable gas recovery and low resource efficiency.
method Developed optimal portfolios of well designs based on reservoir conditions and probabilities.
result Remarkable reduction in variation and substantial increase in energy efficiency achieved.
We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.
New method fractures hyperbolic manifolds using cone singularities.
problem Deforming hyperbolic manifolds with cone singularities.
method Direct manipulation of a fundamental polyhedron to change cone angles.
result Upper unknotting tunnels of highly twisted links can be drilled out.
Universal model for soft tissue mechanics under shock waves.
problem Modeling shock wave mechanics in soft biological tissues.
method Continuum mixture theory with phase-field mechanics.
result Universal thermodynamically consistent formulation for soft porous tissues.
DCGANs generate drainage networks quickly from samples.
problem High computational costs in generating large numbers of drainage networks.
method DCGANs trained with connectivity-informed directional information.
result Connectivity-informed DCGANs outperform other methods in reproducing accurate drainage networks.
DAFNO learns surrogates for complex systems on irregular geometries.
problem Learning accurate surrogates for complex physical systems on irregular geometries.
method DAFNO incorporates a smoothed characteristic function in the integral layer architecture of FNOs, leveraging FFT for rapid computations.
result DAFNO achieves state-of-the-art accuracy on material modeling and airfoil simulation datasets.
Paper develops a classification method using matrix-variate t-distributions.
problem Classifying matrix-valued observations with dependence structure.
method Develops an Expectation-Maximization algorithm for discriminant analysis.
result Method shows promise on various datasets.
We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability …
Deep learning model reconstructs material microstructures from feature representations.
problem Reconstructing complex material microstructures accurately and efficiently.
method Convolutional deep belief network for automated feature learning and dimension reduction.
result Material reconstructions preserve microstructural features and material properties.
The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for uncertainties in the subsurface system and site-specific details. Numerical simulations…
CRED detects microearthquakes efficiently and reliably.
problem Detecting small and weak earthquake signals in noisy data.
method Deep neural network combining convolutional and recurrent units.
result 99.95 F-score on validation data, detects microearthquakes far from training region.
CNNs improve automatic femur bone segmentation from MR images.
problem Manual segmentation of bone MR images is time-consuming and impractical.
method Deep convolutional neural networks (CNNs) trained on volumetric structural MR images of the proximal femur.
result CNNs achieved high segmentation accuracy (dice similarity score of 0.94±0.05). Two Ricci curvature discretizations correlate in complex networks.
problem Comparing two Ricci curvature definitions for complex networks.
method Empirical comparison of Forman-Ricci and Ollivier-Ricci curvatures.
result Forman-Ricci curvature correlates highly with Ollivier-Ricci curvature in real-world networks.
Neural networks learn discrete tasks on continuous data via emergent geometry.
problem Understanding how neural networks perform discrete computations on continuous data.
method Analysis of Riemannian pullback metric across neural network layers.
result Neural networks learn to discretize continuous inputs and perform logical operations on these discretized variables.
Deep learning boosts micro-CT image resolution and texture recovery.
problem Compensating for image resolution trade-offs in micro-CT imaging.
method EDSRGAN trained on a diverse dataset of uCT images.
result EDSRGAN outperforms other methods in texture recovery and resolution.
Graph neural nets improve discrete choice modeling with network effects.
problem Modeling network effects in discrete choice problems.
method Graph Convolutional Neural Network (GCNN) architecture.
result Higher predictive performance than standard models with interpretability.
Deep switch networks generate discrete data and language.
problem Generating high-dimensional discrete data and natural language.
method Adaptive switches model conditional distributions of discrete random variables. Maximum-likelihood objective function training with stochastic gradient descent.
result Stable and interpretable training of deep networks without backpropagation.
Paper proposes an efficient algorithm for learning sparse Bayesian networks from discrete high-dimensional data.
problem Learning sparse structure Bayesian networks from high-dimensional discrete data.
method Score function for sparse DAG, block-wise stochastic coordinate descent with variance reduction.
result The proposed algorithm outperforms existing methods in synthetic data benchmarks.
Proposes a model combining order book data and herd behavior to replicate long-range memory in financial returns.
problem Replicating long-range memory in financial returns and trading activity.
method Combines empirical order book data and financial herd behavior model.
result Model successfully replicates long-range memory in absolute returns and trading activity.
GANs use Gumbel-softmax for generating sequences of discrete elements.
problem GANs struggle with discrete sequences due to non-differentiability of multinomial distributions.
method Used Gumbel-softmax distribution as a continuous approximation to a multinomial distribution for discrete elements.
result GANS with Gumbel-softmax outperform traditional GANs in generating sequences of discrete elements.
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
Derives EoM for DNNs to describe GD dynamics precisely.
problem Gaps between differential equations and actual DNN learning dynamics due to discretization error.
method Starts from GF, derives counter term to cancel discretization error, obtains EoM.
result EoM precisely describes GD dynamics of DNNs, highlights differences between continuous and discrete GD.
A method for disentangling discrete and continuous factors of data without using a discriminator network.
problem Unsupervised disentanglement of discrete and continuous factors of data.
method A procedure that minimizes total correlation of continuous latent variables and a separate discrete inference procedure.
result The method significantly outperforms current disentanglement methods based on disentanglement score and inference network classification score.
Rewiring networks using discrete geometry improves GNN training accuracy and reduces runtime.
problem Inefficient information propagation between distant nodes in graph neural networks.
method Discrete analogues of classical geometric curvature to model and rewire networks.
result Classical geometric notions achieve state-of-the-art GNN training accuracy and significantly reduce runtime.
Discretizing input space improves DLN robustness against adversarial attacks.
problem Improving machine learning models' resistance to adversarial attacks.
method Input discretization and Binary Neural Networks (BNNs).
result 2-bit input discretization significantly enhances adversarial robustness with minimal accuracy loss.
New framework optimizes neural networks using ODEs instead of discrete methods.
problem Optimizing neural networks using discrete methods.
method Port-Hamiltonian approach to learning neural networks.
result Ensures convergence to minimum of objective function.
Neural networks' feature geometry evolves like discrete Ricci flow.
problem Understanding neural feature representations and their geometric transformations.
method Approximating input manifold with geometric graphs and analyzing their evolution during training.
result Neural feature geometry evolves like discrete Ricci flow, with nonlinear activations playing a crucial role.
Proposes OC4Seq for detecting anomalies in discrete event sequences.
problem Challenges in detecting anomalies in discrete event sequences, including data imbalance, discrete events, and sequential nature.
method Integrates anomaly detection with recurrent neural networks (RNNs) to embed sequences into latent spaces and designs a multi-scale RNN framework to capture multi-scale sequential patterns.
result OC4Seq consistently outperforms various baselines on three benchmark datasets.
D2D-SPL uses discrete states and a classifier to train RL faster.
problem Training neural networks in RL due to correlated samples.
method Discretizes state space, uses actor-critic, selects input/target pairs, trains classifier.
result Trains faster than state-of-the-art methods.
New methods for inferring, predicting, and estimating continuous-time, discrete-event processes.
problem Inferring, predicting, and estimating entropy rate of continuous-time, discrete-event processes.
method Bayesian structural inference extended with neural networks.
result Methods are competitive for prediction and entropy-rate estimation with state-of-the-art.
Unified framework for ternary neural networks reduces memory and computation.
problem Training deep neural networks with limited precision and memory.
method Discretization of activations and weights, derivative approximation, and state transition constraints.
result Ternary networks can be reduced to sparse binary networks, termed GXNOR-Nets.
Library learns Bayesian networks from mixed data without discretization.
problem Learning Bayesian networks from mixed data (discrete and continuous variables).
method Proposes an algorithm for structural and parameter learning of Bayesian networks from mixed data using a mixed MI score function and Gaussian approximation. Offers two graph structure enumeration algorithms.
result Advantages in solving approximation and gap recovery problems on synthetic and real datasets.
New method reparameterizes discrete variables to reduce gradient variance.
problem Low variance gradient estimation for discrete variables in neural networks.
method Marginalizing out the variable of interest to bypass discontinuity, resulting in a new reparameterization trick.
result The new reparameterization reduces gradient variance significantly, theoretically not larger than likelihood-ratio method.