A Hybrid Simulation of DNN-based Gray Box Models

Authors: Aayushya Agarwal, Yihan Ruan, Lawrence Pileggi
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: gray box modeling, simulation, neural networks

Abstract:
Simulation is vital for scientific and engineering disciplines, as it enables the prediction and design of physical systems. However, the computational challenges inherent to large-scale simulations often arise from complex device models featuring high degrees of nonlinearities or hidden physical behaviors not captured by first principles. Gray-box models that combine deep neural networks (DNNs) with physics-based models have been proposed to address the computational challenges in modeling complex physical systems. A well-crafted gray box model capitalizes on the interpretability and accuracy of a physical model while incorporating deep neural networks to capture hidden physical behaviors and mitigate computational load associated with highly nonlinear components. Previously, gray box models have been constructed by defining an explicit combination of physics-based and black-box models to represent the behavior of sub-systems; however this alone cannot represent the coupled interactions that define the behavior of the entire physical system. We, therefore, explore an implicit gray box model, where both DNNs (trained on measurement and simulated data) and physical equations share a common set of state-variables. While this approach captures coupled interactions at the boundary of data-driven and physics-based models, simulating the implicit gray box model remains an open-ended problem. In this work, we introduce a new hybrid simulation that directly integrates DNNs into the numerical solvers of simulation engines to fully simulate implicit gray box models of large physical systems. This is accomplished by backpropagating through the DNN to calculate specific Jacobian values during each iteration of the numerical method. The hybrid simulation of implicit gray-box models improves the accuracy and runtime compared to full physics-based simulation and enables reusable DNN models with lower data requirements for training. For demonstration, we explore the advantages of this approach as compared to physics-based, black box, and other gray box methods for simulating the steady-state and electromagnetic transient behavior of power systems.

Decision: desk rejected
Reviewer scores: 6, 1, 5, 5, 3

Reviews and discussion:
<thread>
creation date:
1730325514768

thread_type:
official_review

<thread_object>
creator: reviewer_ukah

<content>
summary:
The paper proposes a hybrid simulation framework to simulate implicit gray-box models for power systems by embedding DNNs into numerical solutions for Jacobian matrix calculations.

strengths:
The paper addresses a relevant problem by aiming to balance computational efficiency with accurate modeling of complex physical systems.

weaknesses:
1. Lack of Novelty. The proposed method lacks significant novelty, as leveraging deep learning models to accelerate or enhance simulations has been widely explored. Specifically, the use of DNNs for Jacobian matrix computation via PyTorch’s autograd is functional but does not represent a novel or impactful contribution relative to established techniques in the field.
2. Limited Comparison over Well-Established Techniques. The experimental analysis is limited primarily to power system simulations, with insufficient benchmarking against state-of-the-art hybrid or physics-informed neural network methods across other domains.
3. Formatting and Clarity Issues. The paper has formatting and clarity issues that impact readability, with Figure 1 being a notable example. The figure lacks clarity and is poorly formatted.

questions:
Please see Weaknesses.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730580604010

thread_type:
official_review

<thread_object>
creator: reviewer_fxjv

<content>
summary:
The authors propose a grey-box model for physical simulation that combines DNN and physics-based modeling. They propose to use a parallel grey box architecture where the physical and the DNN equations share the same/similar state variables, requiring their simultaneous solution. The authors claim that this combination leads to improved accuracy of physical simulation compared to the state-of-the-art.

strengths:
The idea of using the new equation (equation 3) for grey box simulation is interesting and novel. The paper is well written and does not suffer from grammatical issues.

weaknesses:
1. The motivation behind equation 3 is not clear. Why are the physical and the neural network equations being summed up? The physical equation calculates its own value as it is supposed to be the complete picture of the device/system, and the neural network equation also calculates its own value and is supposed to be a complete picture of the device/system. Previous work by Menesklou et al., "Grey box modeling of decanter centrifuges by coupling a numerical process model with a neural network," as a reference in this paper, utilized a summation because the neural network part provides a correction to the physics-based model. The authors need to explain clearly why the two values are being summed up if no error correction is being made. 

2. The example used in "5.1 VALIDATING JACOBIAN ELEMENTS OF THE IMPLICIT DNN-BASED GRAY BOX MODELS" looks like a simple sinusoidal. A neural network learning the sinusoidal function does not seem very impressive. A more complicated system should be chosen to convince me. 

3. The advantages of the methods are not convincing. The experimental results show that the method works but does not compare it to other methods.

questions:
None
</content>
</thread_object>

</thread>
<thread>
creation date:
1730685268265

thread_type:
official_review

<thread_object>
creator: reviewer_7zpb

<content>
summary:
This work suggests a hybrid simulation method called implicit gray box model which combines physics and deep neural networks. The gray-box model shows enhanced accuracy and reduced runtime in power grid simulations.

strengths:
* The gray box model successfully calculate both current values and sensitivities.
* This approach provides simulation  results with more realistic and feasible results that satisfy physical constraints.

weaknesses:
* The experimental example is limited to a single 14-bus network. It would be beneficial to include more standard benchmarks used in previous literature.
* The benchmark results are also limited, comparing only the PQ model, hybrid simulation, and ground truth.
* This work does not provide an in-depth analysis of how the model scales with increasing network size or complexity.

questions:
* The figures should be presented more neatly. For example, a general caption for Figure 1 would be helpful. In Figure 2, the legend colors do not match the actual colors in the graphs.
* The standard table format should be followed. e.g. no vertical lines
</content>
</thread_object>

</thread>
<thread>
creation date:
1730696695611

thread_type:
official_review

<thread_object>
creator: reviewer_mdmx

<content>
summary:
The paper proposes a hybrid simulation approach that integrates neural networks with physics-based models to enhance accuracy and efficiency. It introduces an implicit gray-box model, where deep neural networks (DNNs) and physical equations share state variables. This implicit integration captures complex coupled interactions and reduces training data requirements. The effectiveness of this approach is demonstrated through simulations of steady-state and transient behaviors in power systems.

strengths:
This paper presents an implicit hybrid model method for physics-based models and NN-based models. The NN-based models can help extract sensitivity terms and help with the convergence.

weaknesses:
1. Although the motivation of this paper is good, it is hard to know whether the proposed method is effective in more general and challenging problems. Only the power system example is not sufficient. More challenging and 3D transient examples are needed. Strong and clear examples with enough evidence are required.
2. This paper claims to focus on large-scale systems, but there are no descriptions of the degrees of freedom of the demonstration example. 
3. The literature review is not comprehensive. Only PINN (line 123) is mentioned in the paper. A comprehensive literature is needed, such as Fourier neural operator, DeepONet, JAX-CFD, and other physics-informed machine learning methods.
4. Typo: Lin369, there is no Figure 11.

questions:
1. Since the NN-based model is used for computing Newton-Raphson and integrated with the physics-based model for internal optimization, the accuracy can be better (Figure 3 and Table 1). How about the performance of the traditional physics-based model in Figure 3 and Table 1? 
2. How to deal with noisy data with the proposed method? How to effectively separate noise and real hidden physics? This will strongly influence the optimization of NN.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730881130980

thread_type:
official_review

<thread_object>
creator: reviewer_6xvb

<content>
summary:
In this work, author try to augment simulator with DNN to learn hidden non-linear dynamics not captured by first principle solver. 
prior work explicitly define a system of simulator + DNN learned residual. 
this work propose an implicit combination of simulator and dnn modules, integrate a dnn into the numerical solver.

strengths:
- introduce hybrid simulation engine that integrate DNN into numerical methods to enable reusable and data-efficient learned modules. 
- hybrid method with more accuracy grounding 
- speed up simulation by model complex part with DNN

weaknesses:
demonstrate on relative simple physics-based model, not sure how this work for more complex system with non-linear/complex physics-based simulator.

questions:
- could this framework be integrated into other simulation engines, are there any constraints on this?
- since here one need to backpropagation through the DNN within the numerical solver, would it be a bottleneck for large system?
- how does it work for complex simulation on meshes?
</content>
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</thread>


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