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This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental representation of a reaction-diffusion system with both simplicity and significance. The focus lies specifically in investigating Fisher's equation under conditions of large reaction rate coefficients, wherein solutions manifest as traveling waves, posing a challenge for numerical methods due to the occurring steepness of the wave front. To address optimization challenges associated with the standard PINN approach, a residual weighting scheme is introduced. This scheme is designed to enhance the tracking of propagating wave fronts by considering the reaction term in the reaction-diffusion equation. Furthermore, a specific network architecture is studied which is tailored for solutions in the form of traveling waves. Lastly, the capacity of PINNs to approximate an entire family of solutions is assessed by incorporating the reaction rate coefficient as an additional input to the network architecture. This modification enables the approximation of the solution across a broad and continuous range of reaction rate coefficients, thus solving a class of reaction-diffusion systems using a single PINN instance., Comment: 14 pages, 7 figures

We present a data-driven car occupancy detection algorithm using ultra-wideband radar based on the ResNet architecture. The algorithm is trained on a dataset of channel impulse responses obtained from measurements at three different activity levels of the occupants (i.e. breathing, talking, moving). We compare the presented algorithm against a state-of-the-art car occupancy detection algorithm based on variational message passing (VMP). Our presented ResNet architecture is able to outperform the VMP algorithm in terms of the area under the receiver operating curve (AUC) at low signal-to-noise ratios (SNRs) for all three activity levels of the target. Specifically, for an SNR of -20 dB the VMP detector achieves an AUC of 0.87 while the ResNet architecture achieves an AUC of 0.91 if the target is sitting still and breathing naturally. The difference in performance for the other activities is similar. To facilitate the implementation in the onboard computer of a car we perform an ablation study to optimize the tradeoff between performance and computational complexity for several ResNet architectures. The dataset used to train and evaluate the algorithm is openly accessible. This facilitates an easy comparison in future works., Comment: v1 (17.11.2023). 6 pages, 5 figures

Flamelet models are widely used in computational fluid dynamics to simulate thermochemical processes in turbulent combustion. These models typically employ memory-expensive lookup tables that are predetermined and represent the combustion process to be simulated. Artificial neural networks (ANNs) offer a deep learning approach that can store this tabular data using a small number of network weights, potentially reducing the memory demands of complex simulations by orders of magnitude. However, ANNs with standard training losses often struggle with underrepresented targets in multivariate regression tasks, e.g., when learning minor species mass fractions as part of lookup tables. This paper seeks to improve the accuracy of an ANN when learning multiple species mass fractions of a hydrogen (\ce{H2}) combustion lookup table. We assess a simple, yet effective loss weight adjustment that outperforms the standard mean-squared error optimization and enables accurate learning of all species mass fractions, even of minor species where the standard optimization completely fails. Furthermore, we find that the loss weight adjustment leads to more balanced gradients in the network training, which explains its effectiveness., Comment: 8 pages. Part of Scientific Computing 2023 Conference Proceedings (ISBN e-Book: 978-3-903318-20-5)

The turbulent jet ignition concept using prechambers is a promising solution to achieve stable combustion at lean conditions in large gas engines, leading to high efficiency at low emission levels. Due to the wide range of design and operating parameters for large gas engine prechambers, the preferred method for evaluating different designs is computational fluid dynamics (CFD), as testing in test bed measurement campaigns is time-consuming and expensive. However, the significant computational time required for detailed CFD simulations due to the complexity of solving the underlying physics also limits its applicability. In optimization settings similar to the present case, i.e., where the evaluation of the objective function(s) is computationally costly, Bayesian optimization has largely replaced classical design-of-experiment. Thus, the present study deals with the computationally efficient Bayesian optimization of large gas engine prechambers design using CFD simulation. Reynolds-averaged-Navier-Stokes simulations are used to determine the target values as a function of the selected prechamber design parameters. The results indicate that the chosen strategy is effective to find a prechamber design that achieves the desired target values., Comment: 9 pages. Part of Scientific Computing 2023 Conference Proceedings (ISBN e-Book: 978-3-903318-20-5)

This paper empirically studies commonly observed training difficulties of Physics-Informed Neural Networks (PINNs) on dynamical systems. Our results indicate that fixed points which are inherent to these systems play a key role in the optimization of the in PINNs embedded physics loss function. We observe that the loss landscape exhibits local optima that are shaped by the presence of fixed points. We find that these local optima contribute to the complexity of the physics loss optimization which can explain common training difficulties and resulting nonphysical predictions. Under certain settings, e.g., initial conditions close to fixed points or long simulations times, we show that those optima can even become better than that of the desired solution., Comment: 22 pages

This paper introduces a method for the detection of knock occurrences in an internal combustion engine (ICE) using a 1D convolutional neural network trained on in-cylinder pressure data. The model architecture was based on considerations regarding the expected frequency characteristics of knocking combustion. To aid the feature extraction, all cycles were reduced to 60{\deg} CA long windows, with no further processing applied to the pressure traces. The neural networks were trained exclusively on in-cylinder pressure traces from multiple conditions and labels provided by human experts. The best-performing model architecture achieves an accuracy of above 92% on all test sets in a tenfold cross-validation when distinguishing between knocking and non-knocking cycles. In a multi-class problem where each cycle was labeled by the number of experts who rated it as knocking, 78% of cycles were labeled perfectly, while 90% of cycles were classified at most one class from ground truth. They thus considerably outperform the broadly applied MAPO (Maximum Amplitude of Pressure Oscillation) detection method, as well as other references reconstructed from previous works. Our analysis indicates that the neural network learned physically meaningful features connected to engine-characteristic resonance frequencies, thus verifying the intended theory-guided data science approach. Deeper performance investigation further shows remarkable generalization ability to unseen operating points. In addition, the model proved to classify knocking cycles in unseen engines with increased accuracy of 89% after adapting to their features via training on a small number of exclusively non-knocking cycles. The algorithm takes below 1 ms (on CPU) to classify individual cycles, effectively making it suitable for real-time engine control., Comment: accepted for publication in IEEE/ASME Transactions on Mechatronics. (c) IEEE 2022

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that PINNs are difficult to train and often require a careful tuning of loss weights when data and physics loss functions are combined by scalarization of a multi-objective (MO) problem. In this paper, we aim to understand how parameters of the physical system, such as characteristic length and time scales, the computational domain, and coefficients of differential equations affect MO optimization and the optimal choice of loss weights. Through a theoretical examination of where these system parameters appear in PINN training, we find that they effectively and individually scale the loss residuals, causing imbalances in MO optimization with certain choices of system parameters. The immediate effects of this are reflected in the apparent Pareto front, which we define as the set of loss values achievable with gradient-based training and visualize accordingly. We empirically verify that loss weights can be used successfully to compensate for the scaling of system parameters, and enable the selection of an optimal solution on the apparent Pareto front that aligns well with the physically valid solution. We further demonstrate that by altering the system parameterization, the apparent Pareto front can shift and exhibit locally convex parts, resulting in a wider range of loss weights for which gradient-based training becomes successful. This work explains the effects of system parameters on MO optimization in PINNs, and highlights the utility of proposed loss weighting schemes., Comment: 11 pages

The canonical correlation analysis (CCA) is commonly used to analyze data sets with paired data, e.g. measurements of gene expression and metabolomic intensities of the same experiments. This allows to find interesting relationships between the data sets, e.g. they can be assigned to biological processes. However, it can be difficult to interpret the processes and often the relationships observed are not related to the experimental design but to some unknown parameters. Here we present an extension of the penalized CCA, the supervised penalized approach (spCCA), where the experimental design is used as a third data set and the correlation of the biological data sets with the design data set is maximized to find interpretable and meaningful canonical variables. The spCCA was successfully tested on a data set of Arabidopsis thaliana with gene expression and metabolite intensity measurements and resulted in eight significant canonical variables and their interpretation. We provide an R-package under the GPL license.