Reduced order modeling of energetic materials using physics-aware neural networks.
problem Simulating complex spatiotemporal dynamics in energetic materials.
method Physics-aware recurrent convolutions (PARC) combined with latent space projection to accelerate model training and inference.
result Significant decrease in training and inference time with comparable accuracy.
Bayesian Entropy Neural Networks enforce constraints on deep learning predictions.
problem Deep learning models lack well-defined constraints in their outputs.
method Bayesian Entropy Neural Networks (BENN) using Maximum Entropy principles and the method of multipliers.
result BENN improves model robustness and reliability across various applications.
PANIS learns PDE surrogates for heterogeneous materials without solving the PDE.
problem Learning surrogates for parametrized PDEs in heterogeneous media.
method Physics-aware neural implicit solvers combining probabilistic learning and physics-informed discretization.
result Learned surrogates for effective solutions in heterogeneous materials without solving the reference problem.
The paper develops a physics-aware method for modeling multiscale dynamics with reduced data.
problem Discovering effective, lower-dimensional models for high-dimensional dynamical systems.
method Probabilistic deep neural networks incorporating physical constraints.
result The method reduces the need for extensive multiscale simulations (Small Data regime).
Gaussian processes enhance EO with accurate and uncertain predictions.
problem Challenges in GP models for EO, including data-driven physics and causal inference.
method Data-driven physics-aware models respecting signal characteristics and physical laws.
result GP models need to evolve for better EO applications.
This work develops machine learning for micromagnetic energy minimization.
problem Minimizing Gibbs free energy in full 3D micromagnetic simulations.
method Advanced machine learning techniques, including Physics-Informed Neural Networks (PINNs) and Extreme Learning Machines (ELMs), with reformulated bounds and optimization schemes.
result Competitive performance of machine learning methods compared to traditional numerical approaches.
Compact models learn photocurrent dynamics from radiation-induced excess carrier density.
problem Accurate but computationally expensive physics-based photocurrent models for semiconductor devices.
method Dynamic Mode Decomposition (DMD) for learning reduced order models from internal state data.
result Physics-aware, compact delayed photocurrent models accurately approximate internal excess carrier dynamics.
Framework uses physics knowledge to improve spatiotemporal prediction with limited data.
problem Challenges in modeling physical systems with limited real-world data.
method Physics-aware meta-learning with auxiliary tasks, incorporating PDE-independent spatial and temporal modules.
result Framework outperforms in spatiotemporal prediction tasks with limited data.
Unified framework for forward and inverse PDE problems in multiphase media.
problem Non-differentiable inverse problems in discrete-valued material fields.
method GenPANIS: Latent-variable generative framework preserving discrete microstructures.
result Unified bidirectional inference with minimal labeled pairs and physics-aware decoder.
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
Proposes a transformer model with geostatistical inductive bias for spatio-temporal forecasting.
problem Combining probabilistic rigor of geostatistics with flexible deep learning representations.
method Spatially-informed transformer with learnable covariance kernel.
result Successfully recovers spatial decay parameters end-to-end via backpropagation.
A GPU-based workflow for building physics emulators of hypersonic flows
problem Resolving complex physical phenomena in hypersonic flows
method Fully GPU-based workflow integrating accelerated data generation and neural emulators
result Physics emulators remain reliable beyond their training distribution
Molecular machine learning has been maturing rapidly over the last few years. Improved methods and the presence of larger datasets have enabled machine learning algorithms to make increasingly accurate predictions about molecular properties. However, algorithmic progress has been limited due to the lack of a standard b…
A key problem in computational material science deals with understanding the effect of material distribution (i.e., microstructure) on material performance. The challenge is to synthesize microstructures, given a finite number of microstructure images, and/or some physical invariances that the microstructure exhibits. …
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.
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods are severely inhibited by the high-dimension of the parametric input and the li…
Graphs of neural networks are represented to preserve symmetry, improving performance across various tasks.
problem Lack of equivariance in neural network representations of other neural networks.
method Represent neural networks as computational graphs and use graph neural networks to preserve permutation symmetry.
result Single model encodes diverse neural architectures, outperforming state-of-the-art methods.
Neural networks can approximate functions uniformly across various measures.
problem Universal approximation of functions across different probability measures.
method Proving neural networks are dense in Orlicz spaces, extending classical theorems.
result Neural networks uniformly approximate functions for weakly compact families of measures.
Optimal rates for shallow ReLU networks in nonparametric regression.
problem Approximating smooth and non-smooth functions with shallow ReLU networks.
method Analysis of shallow ReLUk neural networks, using variation norms and deep learning theory. result Optimal approximation rates for shallow ReLU networks in nonparametric regression.
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
Investigates how neural network graph structure impacts predictive performance.
problem Lack of understanding between neural network graph structure and predictive performance.
method Developed relational graph representation to analyze neural networks, identifying a 'sweet spot' for improved performance.
result Identified a 'sweet spot' in relational graph structure that significantly improves neural network predictive performance.
Equivariant neural networks use symmetry to interpret complex data.
problem Interpreting and understanding the behavior of equivariant neural networks.
method Decompose layers into simple representations and analyze nonlinear activation functions.
result Equivariant neural networks can be interpreted using a filtration generalizing Fourier series.
Two new criteria help understand the advantage of deep neural networks.
problem Understanding the advantage of deepening neural networks.
method Proposed two new criteria to evaluate the expressivity of functions computable by deep neural networks.
result Increasing layers is more effective than increasing units in improving the expressivity of deep neural networks.
Paper benchmarks quantum neural networks against classical ones for binary classification tasks.
problem Comparing quantum neural networks with classical ones for binary classification.
method Evaluated with two toy examples, focusing on model complexity and training data size.
result EQNN and QNN outperform ENN and DNN for smaller parameter sets and training data samples.
Secret neural networks hidden within trained models.
problem Excess capacity in neural networks allows embedding secret models.
method Novel framework for hiding secret neural networks within carrier networks.
result Detection of hidden networks is computationally infeasible.
The paper proves consistency of neural networks with regularization.
problem Overfitting in neural networks with large scale data.
method Theoretical framework of neural networks with regularization, sieves method, and minimal neural networks theory.
result The estimated neural network converges to the true underlying function as sample size increases.
New proof shows neural networks can represent all multivariate functions.
problem Representing all multivariate functions with neural networks.
method Proved that three-layer neural networks can represent both continuous and discontinuous functions.
result Three-layer neural networks can represent all multivariate functions, including discontinuous ones.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
DeepWeightFlow generates diverse neural network weights efficiently.
problem Generating complete neural network weights efficiently and accurately.
method Flow Matching in weight space with Git Re-Basin and TransFusion.
result DeepWeightFlow generates high-accuracy neural networks without fine-tuning.
Neural networks improve nonparametric regression with measurement errors.
problem Nonparametric regression with measurement errors.
method Proposes a neural network design using FNN, normalizing flow, and inference network.
result Neural network approach is more flexible and superior or comparable to classical methods.
Graph Metanetworks process diverse neural architectures efficiently.
problem Processing diverse neural architectures efficiently.
method Builds metanetworks using graph neural networks to process graphs representing input neural networks.
result Proves GMNs are expressive and equivariant to parameter permutation symmetries.
A powerful network teaches a weak one, improving its performance.
problem Improving the performance of a weak neural network using a more powerful one.
method During training, a weak network learns features from a strong network to minimize feature distance.
result A weak neural network can increase its performance by learning from a more powerful network.
Affine spiking neural networks learn efficiently and generalize well.
problem Learning with spiking neural networks, especially with positive weights.
method Affine encoders and decoders, continuous parameter dependence, gradient-based training.
result Affine spiking neural networks can approximate shallow ReLU networks and generalize well.
Unified platform SOCRATES for neural network analysis.
problem Analyzing neural networks for bugs and fairness.
method Standardized format, assertion language, and multiple analysis algorithms.
result Unified platform for neural network analysis.
Explains equivariant neural networks for machine learning.
problem Understanding equivariance in neural networks.
method Simple mathematical treatment of neural network concepts.
result Clarifies the mathematical basis of equivariant neural networks.
Research on neural networks has gained significant momentum over the past few years. Because training is a resource-intensive process and training data cannot always be made available to everyone, there has been a trend to reuse pre-trained neural networks. As such, neural networks themselves have become research data.…
Neural networks are mathematically represented via quiver representations.
problem Understanding how neural networks process data and create representations.
method Representing neural networks as quiver representations with activation functions.
result Neural networks' computations can be studied algebraically and geometrically.
Adapting robust statistics to neural networks, researchers found neural networks can be more robust with certain loss functions.
problem The robustness of neural networks in complex learning tasks.
method Adapting the regression breakdown point from robust statistics to neural networks and comparing different configurations and contamination settings.
result Neural networks can benefit from robust loss functions, as demonstrated in extensive simulations.
Paper introduces a noise-robust classification method using hypergraph neural networks.
problem Noisy label learning problem in image datasets.
method PCA for dimensionality reduction, then applies graph-based semi-supervised learning methods including hypergraph neural network.
result Our proposed hypergraph neural network achieves the best performance when noise level increases.
Generative framework learns effective, lower-dimensional models from high-dimensional data.
problem Predicting long-term behavior of complex, multiscale systems with limited data.
method Physics-aware probabilistic model order reduction with latent variables.
result Guaranteed long-term stability and predictive accuracy in multiscale physical systems.
Paper introduces new neural network models and theories.
problem Understanding neural networks beyond over-parameterized regime.
method Develops two exact models and a novel representor theory.
result Provides insights into neural network training and kernel evolution.
New neural networks combine additive regression with traditional architectures.
problem Performance limitations and high parameter requirements of traditional neural networks.
method Introduce hybrid deep additive neural networks with simpler activation and basis functions.
result Hybrid neural networks achieve better performance with fewer parameters.
QRPNNs use quaternion-valued recurrent correlation neural networks to solve cross-talk issues.
problem Cross-talk problem in QRCNNs.
method Combining non-local projection learning with QRCNNs.
result QRPNNs exhibit greater storage capacity and noise tolerance.
New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
Quadratic models explain neural network behavior during training.
problem Understanding neural network dynamics during training with large learning rates.
method Developed and tested Neural Quadratic Models.
result Neural Quadratic Models exhibit the 'catapult phase' similar to neural networks.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…
Probabilistic deep learning uses neural networks and models to handle uncertainty.
problem Handling uncertainty in deep learning models.
method Two approaches: probabilistic neural networks and deep probabilistic models.
result TensorFlow Probability library supports both approaches.
Braid theory optimizes neural network structures.
problem Optimizing the architecture of neural networks.
method Using braid theory to describe and construct neural network structures.
result Braid-based networks outperform other architectures in classification tasks.