TgAE constructs surrogates for inverse modeling with theory-guided training.
problem Creating accurate surrogates for inverse modeling with limited data.
method Theory-guided Auto-Encoder (TgAE) framework based on CNN architecture.
result TgAE surrogate achieves satisfactory accuracy and efficiency in uncertainty quantification and parameter inversion.
Proposes TgNN-LD to improve neural network effectiveness and efficiency.
problem Limits in maintaining tradeoff between data and domain knowledge.
method Converts loss function to constrained form with PDEs, ECs, and EK as constraints, incorporating Lagrangian variables for equitable tradeoff.
result Improves prediction accuracy and conserves resources.
Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of da…
Efficiently quantifies uncertainty in subsurface flow using neural networks guided by theory.
problem Uncertainty in dynamic subsurface flow predictions.
method Theory-guided Neural Network (TgNN) for efficient uncertainty quantification.
result TgNN surrogate improves efficiency of uncertainty quantification compared to MC method.
Tackles dynamic subsurface flow via GAN with physical theory constraints.
problem Deep learning of dynamic subsurface flow with heterogeneous parameters.
method Theory-guided generative adversarial network (TgGAN) for PDEs.
result TgGAN predicts future subsurface flow responses robustly and efficiently.
New framework learns interaction rules from animal trajectories.
problem Challenges in extracting interaction rules from animal movement data.
method Augmented behavioral models with neural networks and theory-guided regularization.
result Improved performance over baselines and novel biological insights.
Active researches are currently being performed to incorporate the wealth of scientific knowledge into data-driven approaches (e.g., neural networks) in order to improve the latter's effectiveness. In this study, the Theory-guided Neural Network (TgNN) is proposed for deep learning of subsurface flow. In the TgNN, as s…
Deep learning upscales geologic models efficiently.
problem Upscaling large-scale geologic models for efficient simulation.
method Theory-guided convolutional neural network (TgCNN) trained to approximate hydraulic conductivity relationships.
result Deep learning method achieves equivalent upscaling accuracy to numerical methods but with significantly improved efficiency.
New method predicts spatio-temporal data with short and long-range dependence.
problem Uncertainty in predicting the distribution of mixed moving average fields.
method Theory-guided machine learning approach using generalized Bayesian algorithm.
result Fixed-time and any-time PAC Bayesian bounds for ensemble forecasts.
A neural network and evolutionary algorithm framework designs nonlinear optical molecules.
problem Designing efficient nonlinear optical materials.
method Multi-stage Bayesian neural network (msBNN) and corrected Lewis-mode group contribution method (cLGC) combined with evolutionary algorithm (EA).
result Accurately and efficiently designs molecules with different optical properties using a small data set.
New method uses neural networks to forecast spatial-temporal data.
problem Probabilistic forecasting of spatio-temporal data with causal structure.
method MMAF-guided learning with ensemble of stochastic feed-forward neural networks.
result Forecasting remains calibrated across multiple time horizons.
New method uses MMAF-guided learning for spatio-temporal probabilistic forecasts.
problem Probabilistic forecasting of spatio-temporal data with causal structure.
method Generalized Bayesian methodology, MMAF-guided learning, ensemble of stochastic feed-forward neural networks.
result Forecast performance comparable to, and sometimes better than, deep learning architectures.
A method to select important experts for Gaussian processes to balance computational efficiency and uncertainty quantification.
problem Balancing computational efficiency and uncertainty quantification in Gaussian processes for big data.
method Using graphical models to select important experts and aggregate their predictions while ensuring uncertainty quantification.
result Substantially reduces computational cost of aggregating dependent experts while ensuring calibrated uncertainty quantification.
Gradient descent converges linearly for neural networks with specific conditions.
problem Optimizing neural networks with fixed width and depth.
method Local Polyak-Lojasiewicz criterion for gradient flow and descent.
result Gradient descent converges to zero-loss solutions under certain conditions.
Algorithm removes specific training data from models efficiently in high-dimensional settings.
problem Efficiently removing specific training data from high-dimensional models without full retraining.
method Starts from original model parameters, performs Newton steps, adds isotropic Laplacian noise.
result Two Newton steps are sufficient for effective unlearning in high-dimensional problems.
Deep ReLU networks can approximate matrix-vector products with error bounds.
problem Can deep ReLU networks accurately approximate matrix-vector products?
method Derived error bounds in Lebesgue and Sobolev norms for deep ReLU FNNs.
result Developed deep approximation theory with successful applications.
IGNIS uses neural networks to estimate copula parameters robustly.
problem Pathological properties of Archimedean copulas make traditional estimators brittle.
method Unified neural estimation framework with multi-input architecture and softplus output layer.
result Accurate and stable estimates for real-world datasets.
New framework for neural network score estimation in diffusion models.
problem Rigorous guarantees for practical score estimation with neural networks.
method Developed a mathematical framework for score estimation with GD-trained neural networks, addressing optimization and generalization.
result Established minimax-optimal generalization bounds for GD-trained neural networks in diffusion models.
Deep learning methods improve subsurface flow modeling efficiency.
problem Efficiently modeling subsurface flow with uncertain parameters.
method Two categories of deep-learning based inverse modeling methods: surrogate-based and direct.
result Deep-learning methods significantly accelerate subsurface flow modeling.
Optimizes seismic monitoring networks using Bayesian OED.
problem Improve seismic event identification and location.
method Bayesian optimal experimental design (OED) to configure sensor networks.
result Optimized sensor network improves seismic event identification and location.