arXiv subjects

Dawen Wu

Publications and source records attributed to Dawen Wu.

4 recordsLinked to original sources

arXiv2024

Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems

The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state variables or result in overparameterized state spaces. Boyuan Chen and his co-authors proposed a neural network model that estimates the degrees of freedom and attempts to discover the state variables of a dynamical system. Despite its innovative approach, this baseline model lacks a connection to the physical principles governing the systems it analyzes, leading to unreliable state variables. This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.

cs.AI↗

arXiv2024

Separable Hamiltonian Neural Networks

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.

cs.LG↗

arXiv2023

Optimization-Informed Neural Networks

Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep learning approach to solve CNLPs. By neurodynamic optimization methods, a CNLP is first reformulated as an initial value problem (IVP) involving an ordinary differential equation (ODE) system. A neural network model is then used as an approximate solution for this IVP, with the endpoint being the prediction to the CNLP. We propose a novel training algorithm that directs the model to hold the best prediction during training. In a nutshell, OINN transforms a CNLP into a neural network training problem. By doing so, we can solve CNLPs based on deep learning infrastructure only, without using standard optimization solvers or numerical integration solvers. The effectiveness of the proposed approach is demonstrated through a collection of classical problems, e.g., variational inequalities, nonlinear complementary problems, and standard CNLPs.

math.OC↗

arXiv2020

Faster Regret Matching

The regret matching algorithm proposed by Sergiu Hart is one of the most powerful iterative methods in finding correlated equilibrium. However, it is possibly not efficient enough, especially in large scale problems. We first rewrite the algorithm in a computationally practical way based on the idea of the regret matrix. Moreover, the rewriting makes the original algorithm more easy to understand. Then by some modification to the original algorithm, we introduce a novel variant, namely faster regret matching. The experiment result shows that the novel algorithm has a speed advantage comparing to the original one.

cs.GT↗