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Found 12 papers, 2 papers with code
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems.
tLaSDI: Thermodynamics-informed latent space dynamics identification
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics.
Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms
The probability distribution of the random vector determines the statistical properties of RFG.
On the training and generalization of deep operator networks
To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network.
GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems
We propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism.
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions.
A Caputo fractional derivative-based algorithm for optimization
We propose three versions -- non-adaptive, adaptive terminal and adaptive order.
Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and Avoidance
No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes.
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in $C^0$.
Effects of Depth, Width, and Initialization: A Convergence Analysis of Layer-wise Training for Deep Linear Neural Networks
We show that when the orthogonal-like initialization is employed, the width of intermediate layers plays no role in gradient-based training, as long as the width is greater than or equal to both the input and output dimensions.
Trainability of ReLU networks and Data-dependent Initialization
In order to quantify the trainability, we study the probability distribution of the number of active neurons at the initialization.
Dying ReLU and Initialization: Theory and Numerical Examples
Numerical examples are provided to demonstrate the effectiveness of the new initialization procedure.
