Learning to Solve Differential Equation Constrained Optimization Problems
Authors: Vincenzo Di Vito Francesco, Mostafa Mohammadian, Kyri Baker, Ferdinando Fioretto
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments across problems in energy optimization and finance modeling show that this method provides full compliance with dynamic constraints and it produces results up to 25 times more precise than other methods which do not explicitly model the system s dynamic equations. |
| Researcher Affiliation | Academia | 1 Department of Computer Science, University Of Virginia, EMAIL 2 College of Engineering and Applied Science, University of Colorado Boulder, EMAIL |
| Pseudocode | Yes | Algorithm 1 Primal Dual Learning for DE-Constrained Optimization |
| Open Source Code | No | The paper mentions that "Our implementation uses neural-ODE (Chen et al., 2018) models Nθ" and that "The AC-OPF models are implemented in Julia and solved using IPOPT (W achter & Biegler, 2006)", referring to third-party tools or methods. However, there is no explicit statement or link indicating that the authors' own code for the described methodology (DE-OP) is publicly available. |
| Open Datasets | Yes | initial asset prices {ζi}n i=1 are obtained from the Nasdaq database (Nasdaq, 2022) to form initial vectors {ζj}10,000 j=1 DE-OP is evaluated on two key power networks, the WSCC 9 and IEEE 57 bus-systems (Babaeinejadsarookolaee et al., 2021), under various operating system conditions |
| Dataset Splits | Yes | split into 80% training, 10% validation, and 10% test sets. The dataset uses an 80/10/10 split. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU models, CPU types, or memory specifications used for running the experiments. |
| Software Dependencies | No | The paper mentions using "Julia" for implementation, "IPOPT (W achter & Biegler, 2006)" and "cvxpy (Diamond & Boyd, 2016)" as solvers, and "Adam optimizer" and "Dopri5" as algorithms/methods. However, it does not provide specific version numbers for these software components or libraries, which is required for a reproducible description. |
| Experiment Setup | Yes | Each neural-ODE model is a fully connected feedforward Re LU neural network with 2 hidden layers, each with 200 units. Each model is trained using Adam optimizer, with default learning rate η = 10-3 and default hyperparameters. Each proxy optimizer model is a fully connected Feed Foward Re LU neural network with 5 hidden layers, each with 200 units. The DE-OP s optimization model Fω and Lagrangian Dual proxy model are trained with a Lagrangian step size ρ = 10-1, while the Lagrangian multipliers λh and λg are updated at each epoch. The stochastic component of the neural SDE, the LSTM and Feed Forward model are each 2-layers Re LU networks, each with 100 units. The neural-SDE, LSTM and Feed Forward models are all trained using Adam optimizer, with default learning rate η = 10-3 and hyperparameters. The final time instant T = 28, 800 seconds which corresponds to 8 hours. Specifically, for each generator g G, the datasets Dg used for training the generator dynamic predictor N g θ , consists of pairs (xi, yi(t)) Dg, where xi = (δg 0, ωg 0, |V g|, θ g) is the input of the neural-ODE model, and yi(t) = (δg(t), ωg(t), |V g|(t), θ g(t)) the corresponding solution of (12) with initial conditions yi(0) = I(xi), represented by (16e)-(16g) and computed using Dopri5, a numerical algorithm implementing an adaptive Runge-Kutta method. At training time, given a pair (xi, yi(t)) Dg, the target is constructed as yg i (t) = yg i (0), yg i ( t), . . . , yg i (n t), with t = 0.001 and the number of points n, is set to 200 at the beginning of the training, and gradually increases up to 1000. This trick allows to avoid local minima during training (Kidger, 2022). At test time, we set n = 1000. |