Kolloquiumsvortrag 17. Dezember 2024, Nikhil Jones (Betreuer: Sommer)
Evaluation of Physics-Informed Neural Networks in Modeling Dynamics of Lumped Parameter Systems
Physics-Informed Neural Networks (PINNs) have gained importance as a powerful method for solving differential equations by integrating neural networks with underlying physical laws. There’s a growing interest in exploring their performance in lumped parameter systems which are governed by ordinary differential equations (ODEs). These systems such as electrical circuits, exhibit complex challenges when transitioning between circuit configurations or when parameter value changes. Traditional neural networks struggle to model these scenarios due to the absence of embedded physics in their learning process. This study aims to evaluate the performance and generalization capabilities of PINNs by including additional parameters along with time t into the input space. A non-stiff Resistor-Capacitor (RC) circuit
model was chosen for the study from which the ODEs were derived. The PINN training utilizes a range of resistance, capacitance and switching conditions as inputs to the model, rather than a fixed value. The training was performed using strategies that randomize these values across collocation points and across epochs. The numeri- cal solution from Runge-Kutta 4th-order solver (RK4) serves as the reference solution.
These ODEs are embedded in the loss function of the PINN. The output calculated from the PINN is then measured by Root Mean Square Error (RMSE) for predicting the accuracy of the model, with Lyapunov function derivative, sensitivity analysis and energy dissipation to assess the dynamical system characteristics. The results obtained show that, training the PINNs with randomized parameter inputs enhances
its ability to generalize well within and slightly beyond the training range. The PINN output was seen to maintain stable and passive behavior across all evaluation scenarios. And also the strategy of training across collocation points achieved better results than across epochs. This study highlights the potential of PINNs to generalize and adapt to different scenarios without extensive retraining.
Zeit: 10:15 Uhr
Ort: Raum 04.137, Martensstr. 3, Erlangen
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Meeting-ID: 683 5070 2053
Kenncode: 647333