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Design optimization of adaptive systems requires a robust analysis method that can accommodate various changes in design and boundary conditions. In this work, physics-informed neural networks (PINNs) are used to approximate solutions to differential equations across a range of problem parameter values. This mesh-free method simply requires residual evaluation at sampling points within the analysis domain and along boundaries, and the training process does not require any reference problem to be solved through conventional solution methods. The trained model can be used to predict the solution field, conduct parameter space analysis and design optimization. Using automatic differentiation, the design objective and their derivatives can be computed as a post process for a gradient-based design optimization. The method is demonstrated in a 1D heat transfer problem governed by the steady-state heat equation. Use of the PINN model for design optimization is illustrated in a problem of finding a material transition location to minimize temperature at a specified location. The PINN model that does not include problem parameters as input can be trained to within 0.05% error. PINN models that involve problem parameters as inputs are more difficult to train, especially when the input-to-output relationship is complex.

A machine learning algorithm that performs multifidelity domain decomposition is introduced. While the design of complex systems can be facilitated by numerical simulations, the determination of appropriate physics couplings and levels of model fidelity can be challenging. The proposed method automatically divides the computational domain into subregions and assigns required fidelity level, using a small number of high fidelity simulations to generate training data and low fidelity solutions as input data. Unsupervised and supervised machine learning algorithms are used to correlate features from low fidelity solutions to fidelity assignment. The effectiveness of the method is demonstrated in a problem of viscous fluid flow around a cylinder at Re ≈ 20. Ling et al. built physics-informed invariance and symmetry properties into machine learning models and demonstrated improved model generalizability. Along these lines, we avoid using problem dependent features such as coordinates of sample points, object geometry or flow conditions as explicit inputs to the machine learning model. Use of pointwise flow features generates large data sets from only one or two high fidelity simulations, and the fidelity predictor model achieved 99.5% accuracy at training points. The trained model was shown to be capable of predicting a fidelity map for a problem with an altered cylinder radius. A significant improvement in the prediction performance was seen when inputs are expanded to include multiscale features that incorporate neighborhood information.

When a periodic waveform with a discrete-harmonic spectrum is temporally windowed to make a signal, its spectrum becomes a continuous function of frequency. However, there are discrete-frequency representations for windowed signals such as the Fourier series representation of a periodically extended signal. This article introduces the concept of matching between the temporal window and the periodic waveform. Matching leads to a discrete-frequency representation in which the Fourier transform of the windowed signal preserves the amplitudes and phases of the waveform on the set of original waveform frequencies. Generating signals with matched window and waveform leads to important control of experiments.

A recently developed implicit wave solver, based on the Method of Lines Transpose, dimensional splitting and a fast 1D integral solution method, removes the CFL condition while maintaining computational cost comparable to explicit wave solvers1,2. We present the application of this wave solver in a particle-in-cell (PIC) method for the simulation of plasmas in an approach that can handle both electrostatic and fully electromagnetic cases by formulating Maxwell's equations as wave equations for potentials in the Lorenz gauge. We describe the coupling of the wave solver to particles, and show the results of some standard one- and two-dimensional electrostatic test problems, and discuss the extension to the fully electromagnetic case.

Summary form only given. Maxwell's equations are an integral part of many plasma models, and therefore robust, efficient solvers are needed in order to attain accurate numerical simulations of plasma. By formulating the Vlasov-Maxwell problem in terms of vector potentials, Maxwell's equation reduces to 4 wave equations, (one for the scalar potential and 3 for the vector potential), forced by the charges and currents as determined by the electron and ion distribution functions. Such problems are challenging because they often involve multiple time and spatial scales, complex geometries, and many particles, which are modeled as moving point sources. Explicit methods are efficient for spatial discretization, but can only take small time steps due to the CFL restriction, and are therefore are unfavorable for long time simulations. We present an implicit, A-stable boundary integral solver (IBIS) for the wave equation, using a method of lines transpose (MOLT) approach. We first build a fast O(N) solver in one spatial dimension, and then extend it to higher dimensions using alternate direction implicit (ADI) splitting, thus maintaining efficiency. This makes our IBIS as efficient as explicit solvers, but additionally allows for larger time steps and thus faster simulations. We can also address complex geometries, moving point sources, and a wide variety of boundary conditions. Additionally, we have implemented domain decomposition, which makes our algorithm flexible for use in adaptive mesh refinement.

High‐resolution (200 kHz sample rate) measurements of interaural coherence for a KEMAR manikin were made in an anechoic environment. As the angle of incident sound was varied in the horizontal plane, there was a minimum in coherence around ±45°. These coherence minima occured at low frequencies, up to about 3000 Hz, and decreased in depth for increasing frequency, f, at a rate approximately proportional to 1/f. In a 1/3‐octave band centered at 500 Hz, the interaural coherence was approximately 0.7 for angles of ±45°. These results were confirmed by measurements in KEMAR using probe microphones. Measurements made using probe microphones with human listeners at angles of ±45° and 0° showed a similar pattern in coherences, but the minima were far more shallow. In the 500 Hz band, a coherence of, on average, 0.94 was measured in listeners facing ±45°, compared to an average coherence of 0.99 in that band at 0°. Headphone experiments using measured values of coherence showed that the deeper measured coherence minima lead to a deficit in sound localization. [Work supported by the NIDCD grant DC00181.]