Deep Learning-Based Analysis of Power Consumption in Gasoline, Electric, and Hybrid Vehicles

Accurate power consumption prediction is crucial for improving efficiency and reducing environmental impact, yet traditional methods relying on specialized instruments or rigid physical models are impractical for large-scale, real-world deployment. This study introduces a scalable data-driven method using powertrain dynamic feature sets and both traditional machine learning and deep neural networks to estimate instantaneous and cumulative power consumption in internal combustion engine (ICE), electric vehicle (EV), and hybrid electric vehicle (HEV) platforms. ICE models achieved high instantaneous accuracy with mean absolute error and root mean squared error on the order of $10^{-3}$, and cumulative errors under 3%. Transformer and long short-term memory models performed best for EVs and HEVs, with cumulative errors below 4.1% and 2.1%, respectively. Results confirm the approach's effectiveness across vehicles and models. Uncertainty analysis revealed greater variability in EV and HEV datasets than ICE, due to complex power management, emphasizing the need for robust models for advanced powertrains.

Physics-Informed Neural Networks: Minimizing Residual Loss with Wide Networks and Effective Activations

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different from those of common supervised problems. Therefore, relying on the existing theory leads to unjustified design choices and suboptimal performance. In this work, we analyze the residual loss by studying its characteristics at critical points to find the conditions that result in effective training of PINNs. Specifically, we first show that under certain conditions, the residual loss of PINNs can be globally minimized by a wide neural network. Furthermore, our analysis also reveals that an activation function with well-behaved high-order derivatives plays a crucial role in minimizing the residual loss. In particular, to solve a $k$-th order PDE, the $k$-th derivative of the activation function should be bijective. The established theory paves the way for designing and choosing effective activation functions for PINNs and explains why periodic activations have shown promising performance in certain cases. Finally, we verify our findings by conducting a set of experiments on several PDEs. Our code is publicly available at https://github.com/nimahsn/pinns_tf2.

Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks

Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs). However, they often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under stochastic gradient descent with momentum (SGDM). This demonstrates SGDM significantly reduces the effect of spectral bias. We have also examined why training a model via the Adam optimizer can accelerate the convergence while reducing the spectral bias. Moreover, our numerical experiments have confirmed that wide-enough networks using SGDM still converge to desirable solutions, even in the presence of high-frequency features. In fact, we show that the width of a network plays a critical role in convergence.