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Found 17 papers, 8 papers with code
Towards a Foundation Model for Partial Differential Equations: Multi-Operator Learning and Extrapolation
More importantly, we provide three extrapolation studies to demonstrate that PROSE-PDE can generalize physical features through the robust training of multiple operators and that the proposed model can extrapolate to predict PDE solutions whose models or data were unseen during the training.
D2NO: Efficient Handling of Heterogeneous Input Function Spaces with Distributed Deep Neural Operators
Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems.
PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers
Approximating nonlinear differential equations using a neural network provides a robust and efficient tool for various scientific computing tasks, including real-time predictions, inverse problems, optimal controls, and surrogate modeling.
Random Feature Models for Learning Interacting Dynamical Systems
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems.
Concentration of Random Feature Matrices in High-Dimensions
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.
SRMD: Sparse Random Mode Decomposition
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis.
HARFE: Hard-Ridge Random Feature Expansion
We prove that the HARFE method is guaranteed to converge with a given error bound depending on the noise and the parameters of the sparse ridge regression model.
SHRIMP: Sparser Random Feature Models via Iterative Magnitude Pruning
Inspired by the success of the iterative magnitude pruning technique in finding lottery tickets of neural networks, we propose a new method -- Sparser Random Feature Models via IMP (ShRIMP) -- to efficiently fit high-dimensional data with inherent low-dimensional structure in the form of sparse variable dependencies.
Conditioning of Random Feature Matrices: Double Descent and Generalization Error
In particular, we show that if the complexity ratio $\frac{N}{m}$ where $N$ is the number of neurons and $m$ is the number of data samples scales like $\log^{-1}(N)$ or $\log(m)$, then the random feature matrix is well-conditioned.
Generalization Bounds for Sparse Random Feature Expansions
In particular, we provide generalization bounds for functions in a certain class (that is dense in a reproducing kernel Hilbert space) depending on the number of samples and the distribution of features.
Reduced Order Modeling using Shallow ReLU Networks with Grassmann Layers
The neural network takes the form of a "three-layer" network with the first layer constrained to lie on the Grassmann manifold and the first activation function set to identity, while the remaining network is a standard two-layer ReLU neural network.
NeuPDE: Neural Network Based Ordinary and Partial Differential Equations for Modeling Time-Dependent Data
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations.
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Extending the step-size restriction for gradient descent to avoid strict saddle points
We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points.
Recovery guarantees for polynomial approximation from dependent data with outliers
In this work, we study the problem of learning nonlinear functions from corrupted and dependent data.
Forward Stability of ResNet and Its Variants
In this work, we show that the post-activation ResNet is related to an optimal control problem with differential inclusions, and provide continuous-time stability results for the differential inclusion associated with ResNet.
On the Convergence of the SINDy Algorithm
In this work, we provide some theoretical results on the behavior and convergence of the algorithm proposed in [6].
Optimization and Control Information Theory Information Theory
Sparse model selection via integral terms
Model selection and parameter estimation are important for the effective integration of experimental data, scientific theory, and precise simulations.
