Search arXivSearch

arXiv · 2304.13799

Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines

Abstract

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance requirements. The PINN model is applied to diesel engines with a variable-geometry turbocharger and exhaust gas recirculation, using measurement data of selected state variables. The results demonstrate the ability of the PINN model to predict simultaneously both unknown parameters and dynamics accurately with both clean and noisy data, and the importance of the self-adaptive weight in the loss function for faster convergence. The input data for these simulations are derived from actual engine running conditions, while the outputs are simulated data, making this a practical case study of PINN's ability to predict real-world dynamical systems. The mean value model of the diesel engine incorporates empirical formulae to represent certain states, but these formulae may not be generalizable to other engines. To address this, the study considers the use of deep neural networks (DNNs) in addition to the PINN model. The DNNs are trained using laboratory test data and are used to model the engine-specific empirical formulae in the mean value model, allowing for a more flexible and adaptive representation of the engine's states. In other words, the mean value model uses both the PINN model and the DNNs to represent the engine's states, with the PINN providing a physics-based understanding of the engine's overall dynamics and the DNNs offering a more engine-specific and adaptive representation of the empirical formulae. By combining these two approaches, the study aims to offer a comprehensive and versatile approach to monitoring the health and performance of diesel engines.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kamaljyoti Nath, Xuhui Meng, Daniel J Smith, George Em Karniadakis. 2023-08-05. Physics-informed neural networks for predicting gas flow dynamics and unknown parameters in diesel engines. https://doi.org/10.1038/s41598-023-39989-4

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

Analysis of Regularized Learning in Banach Spaces for Linear-functional Data

This article delves into the study of the theory of regularized learning in Banach spaces for linear-functional data. It encompasses discussions on representer theorems, pseudo-approximation theorems, and convergence theorems. Regularized learning is designed to minimize regularized empirical risks over a Banach space. The empirical risks are calculated by utilizing training data and multi-loss functions. The input training data are composed of linear functionals in a predual space of the Banach space to capture discrete local information from multimodal data and multiscale models. Through the regularized learning, approximations of the exact solution to an unidentified or uncertain original problem are globally achieved. In the convergence theorems, the convergence of the approximate solutions to the exact solution is established through the utilization of the weak* topology of the Banach space. The theorems of regularized learning are utilized in the interpretation of classical machine learning, such as support vector machines and artificial neural networks.

cs.LG

On Minimal Depth in Neural Networks

Understanding the relationship between the depth of a neural network and its representational capacity is a central problem in deep learning theory. In this work, we develop a geometric framework to analyze the expressivity of ReLU networks with the notion of depth complexity for convex polytopes. The depth of a polytope recursively quantifies the number of alternating convex hull and Minkowski sum operations required to construct it. This geometric perspective serves as a rigorous tool for deriving depth lower bounds and understanding the structural limits of deep neural architectures. We establish lower and upper bounds on the depth of polytopes, as well as tight bounds for classical families. These results yield two main consequences. First, we provide a purely geometric proof of the expressivity bound by Arora et al. (2018), confirming that $\lceil \log_2(n+1)\rceil$ hidden layers suffice to represent any continuous piecewise linear (CPWL) function. Second, we prove that, unlike general ReLU networks, convex polytopes do not admit a universal depth bound. Specifically, the depth of cyclic polytopes in dimensions $n \geq 4$ grows unboundedly with the number of vertices. This result implies that Input Convex Neural Networks (ICNNs) cannot represent all convex CPWL functions with a fixed depth, revealing a sharp separation in expressivity between ICNNs and standard ReLU networks.

cs.LG

ELEMENT: Episodic and Lifelong Exploration via Maximum Entropy

Reinforcement learning agents depend on reward signals whose density is rarely under the designer's control, and when such signals are absent, an agent must generate its own drive to explore. State entropy maximization offers a principled objective for this, but existing methods break down at scale in two ways: the intrinsic reward vanishes once a state has been visited, discouraging revisits to the very gateways that lead onward, and estimating entropy over millions of accumulated observations becomes computationally prohibitive. We address both with Episodic and Lifelong Exploration via Maximum Entropy (ELEMENT), a multiscale intrinsically motivated framework for reward-free exploration that transfers to downstream tasks. ELEMENT couples lifelong entropy maximization with a complementary episodic term acting on a faster timescale. For the episodic term, we derive average episodic state entropy, an intrinsic reward that is the exact minimizer of a tractable upper bound on the reward-decomposition objective; for the lifelong term, we propose a $k$NN graph-based estimator that keeps entropy tractable without forgetting. ELEMENT consistently outperforms state-of-the-art intrinsic reward baselines on state coverage and unsupervised pre-training. Videos, code, and supplementary material: https://sites.google.com/view/element-rl.

cs.LG