Stéphane Lanteri

Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing partial differential equations (PDEs) such as the Helmholtz equation. However, these methods face significant computational challenges when applied to high-frequency wave problems in complex two-dimensional domains. This work investigates Finite Basis Physics-Informed Neural Networks (FBPINNs) and their multilevel extensions as a promising alternative. These methods leverage domain decomposition, partitioning the computational domain into overlapping sub-domains, each governed by a local neural network. We assess their accuracy and computational efficiency in solving the Helmholtz equation for the homogeneous case, demonstrating their potential to mitigate the limitations of traditional approaches.

Physics-Informed Neural Networks (PINNs) are becoming a popular method for solving PDEs, due to their mesh-free nature and their ability to handle high-dimensional problems where traditional numerical solvers often struggle. Despite their promise, the practical application of PINNs is still constrained by several fac- tors, a primary one being their often-limited accuracy. This paper is dedicated to enhancing the accuracy of PINNs by introducing spectral-prior guided multistage strategy. We propose two methods: Spectrum- Informed Multistage Physics-Informed Neural Networks (SI-MSPINNs) and Multistage Physics-Informed Neural Networks with Spectrum Weighted Random Fourier Features (RFF-MSPINNs). The SI-MSPINNs integrate the core mechanism of Spectrum-Informed Multistage Neural Network (SI-MSNNs) and PINNs, in which we extract the Dominant Spectral Pattern (DSP) of residuals by the discrete Fourier transform. This DSP guides the network initialization to alleviate spectral bias, and gradually optimizes the resolution accuracy using a multistage strategy. The RFF-MSPINNs combines random Fourier features with spectral weighting methods, dynamically adjusting the frequency sampling distribution based on the residual power spectral density, allowing the network to prioritize learning high-energy physical modes. Through experimental verification of the Burgers equation and the Helmholtz equation, we show that both models significantly improve the accuracy of the original PINNs.

Beam-steering antennas, based on sub-wavelength deflectors, aim to facilitate information exchange with satellite communication (SatCom) on-the-move systems. Recent beam-deflection solutions are often based on the phase-gradient metasurfaces (PGM) concept to generate the desired wavefront. However, the performance remains inadequate for advanced communication technologies due to bandwidth limitations and insufficient efficiency. Here, a highly-efficient broadband beam-deflection system is design, fabricate, and characterize experimentally for SatCom applications. To achieve that, an advanced Bayesian learning strategy, accompanied by an innovative nonlocal metasurface (NLM) configuration, is employed. This non-trivial broadband design leverages a sophisticated coupling between adjacent sub-wavelength elements, together with varying thicknesses along the propagation direction to manipulate the incoming beam. The novel beam-deflector is illuminated with a circularly polarized wave and is designed to operate in the Ka-Tx band from 27.5 to 31 GHz. The optimized structure demonstrates exceptionally high performance compared to the conventional phase-gradient synthesizing counterparts. The experimental validation exhibits an excellent agreement with the numerical simulation, highlighting the potential of this optimization-assisted design to advance metasurface technology for various beam-steering applications

Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling methods and loss function weights for different PDEs, which reduces the efficiency of the solvers. In this paper, we pro- pose a general multi-stage framework, i.e. BO-SA-PINNs to alleviate this issue. In the first stage, Bayesian optimization (BO) is used to select hyperparameters for the training process, and based on the results of the pre-training, the network architecture, learning rate, sampling points distribution and loss function weights suitable for the PDEs are automatically determined. The proposed hyperparameters search space based on experimental results can enhance the efficiency of BO in identifying optimal hyperparameters. After selecting the appropriate hyperparameters, we incorporate a global self-adaptive (SA) mechanism the second stage. Using the pre-trained model and loss information in the second-stage training, the exponential moving average (EMA) method is employed to optimize the loss function weights, and residual-based adaptive refinement with distribution (RAR-D) is used to optimize the sampling points distribution. In the third stage, L-BFGS is used for stable training. In addition, we introduce a new activation function that enables BO-SA-PINNs to achieve higher accuracy. In numerical experiments, we conduct comparative and ablation experiments to verify the performance of the model on Helmholtz, Maxwell, Burgers and high-dimensional Poisson equations. The comparative experiment results show that our model can achieve higher accuracy and fewer iterations in test cases, and the ablation experiments demonstrate the positive impact of every improvement.

Beam-steering antennas, based on sub-wavelength deflectors, aim to facilitate information exchange with satellite communication (SatCom) on-the-move systems. Recent beam-deflection solutions are often based on the phase-gradient metasurfaces (PGM) concept to generate the desired wavefront. However, the performance remains inadequate for advanced communication technologies due to band- width limitations and insufficient efficiency. Here, a highly-efficient broadband beam-deflection system is design, fabricate, and characterize experimentally for SatCom applications. To achieve that, an advanced Bayesian learning strategy, accompanied by an innovative nonlocal metasurface (NLM) con- figuration, is employed. This non-trivial broadband design leverages a sophisticated coupling between adjacent sub-wavelength elements, together with varying thicknesses along the propagation direction to manipulate the incoming beam. The novel beam-deflector is illuminated with a circularly polarized wave and is designed to operate in the Ka-Tx band from 27.5 to 31GHz. The optimized structure demonstrates exceptionally high performance compared to the conventional phase-gradient synthe- sizing counterparts. The experimental validation exhibits an excellent agreement with the numerical simulation, highlighting the potential of this optimization-assisted design to advance metasurface technology for various beam-steering applications.

We propose a parametric geometry-based non-intrusive model order reduction (NIMOR) model for electromagnetic simulation in domains of different shapes. The free-from-deformation (FFD) method is introduced to adjust the mesh when the shape changes. This NIMOR model generates a set of reduced-order basis (RB) functions by applying a two-step randomized singular value decomposition (SVD) method with an auto-rank generator (ARRSVD) to the matrix composed of the full-order solutions. A map between the time/geometry parameters and the projection coefficients is approximated by the cubic-spline interpolation (CSI) approach. This reduced-order model (ROM) is trained in the offline stage, while the RB solutions for new parameters can be quickly recovered in the online stage. Numerical experiments show that the proposed NIMOR method can achieve near real-time electromagnetic scattering simulation on domains of different shapes while guaranteeing the accuracy.

We present a data-driven surrogate modeling for parameterized electromagnetic simulation. This method extracts a set of reduced basis (RB) functions from full-order solutions through a two-step proper orthogonal decomposition (POD) method. A mapping from the time/parameter to the principal components of the projection coefficients, extracted by canonical polyadic decomposition (CPD), is approximated by a cubic spline interpolation (CSI) approach. The reduced-order model (ROM) is trained in the offline phase, while the RB solution of a new time/parameter value is recovered fast during the online phase. We evaluate the performance of the proposed method with numerical tests for the scattering of a plane wave by a 2-D multi-layer dielectric disk and a 3-D multi-layer dielectric sphere.