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Found 5 papers, 1 papers with code
Estimating the Distribution of Parameters in Differential Equations with Repeated Cross-Sectional Data
With RCS data, we found that traditional methods for parameter estimation in differential equations, such as using mean values of time trajectories or Gaussian Process-based trajectory generation, have limitations in estimating the shape of parameter distributions, often leading to a significant loss of data information.
Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids
There has been growing interest in models that learn the operator from the parameters of a partial differential equation (PDE) to the corresponding solutions.
HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetwork
This study proposes HyperDeepONet, which uses the expressive power of the hypernetwork to enable the learning of a complex operator with a smaller set of parameters.
Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)
By employing Augmented Lagrangian relaxation, the constrained optimization problem becomes a sequential max-min problem so that the learnable parameters $\lambda$ adaptively balance each loss component.
Traveling Wave Solutions of Partial Differential Equations via Neural Networks
This paper focuses on how to approximate traveling wave solutions for various kinds of partial differential equations via artificial neural networks.
Numerical Analysis Numerical Analysis Analysis of PDEs
