Identification of the dynamic characteristics of nonlinear structures

Imperial Users onl

Adaptive weighting of Bayesian physics informed neural networks for multitask and multiscale forward and inverse problems

In this paper, we present a novel methodology for automatic adaptive weighting of Bayesian Physics-Informed Neural Networks (BPINNs), and we demonstrate that this makes it possible to robustly address multi-objective and multi-scale problems. BPINNs are a popular framework for data assimilation, combining the constraints of Uncertainty Quantification (UQ) and Partial Differential Equation (PDE). The relative weights of the BPINN target distribution terms are directly related to the inherent uncertainty in the respective learning tasks. Yet, they are usually manually set a-priori, that can lead to pathological behavior, stability concerns, and to conflicts between tasks which are obstacles that have deterred the use of BPINNs for inverse problems with multi-scale dynamics. The present weighting strategy automatically tunes the weights by considering the multi-task nature of target posterior distribution. We show that this remedies the failure modes of BPINNs and provides efficient exploration of the optimal Pareto front. This leads to better convergence and stability of BPINN training while reducing sampling bias. The determined weights moreover carry information about task uncertainties, reflecting noise levels in the data and adequacy of the PDE model. We demonstrate this in numerical experiments in Sobolev training, and compare them to analytically $\epsilon$-optimal baseline, and in a multi-scale Lokta-Volterra inverse problem. We eventually apply this framework to an inpainting task and an inverse problem, involving latent field recovery for incompressible flow in complex geometries

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems

Nonlinear Equalization and Digital Pre-Distortion Techniques for Future Radar and Communications Digital Array Systems

Modern radar (military, automotive, weather, etc.) and communication systems seek to leverage the spatio-spectral efficiency of phased arrays. Specifically, there is an increasingly large demand for fully-digital arrays, with each antenna element having its own transmitter and receiver. Further, in order to makes these systems realizable, low-cost, low-complexity solutions are required, often sacrificing the system's linearity. Lower linearity paired with the inherent lack of RF spacial filtering can make these highly digital systems vulnerable to high-power interferering signals-- potentially introducing spectral regrowth and/or gain compression, distorting the signal-of-interest. Digital linearization solutions such as Digital Pre-Distiortion (DPD) and Nonlinear Equalization (NLEQ) have been shown to effectively mitigate nonlinearities for transmitters and receivers, respectively. Further, DPD and NLEQ seek to extend the effective dynamic range of digital arrays, helping the systems reach their designed dynamic range improvement of $10\log_{10}(N)$~dB, where $N$ is the number of transmitters/receivers. However, the performance of these solutions is ultimately determined by training model and waveform. Further, the nonlinear characteristics of a system can change with temperature, frequency, power, time, etc., requiring a robust calibration technique to maintain a high-level of nonlinear mitigation. This dissertation reviews the different types of nonlinear models and the current NLEQ and DPD algorithms for digital array systems. Further, a generalized calibration waveform for both NLEQ and DPD is proposed, allowing a system to maximize its dynamic range over power and frequency. Additionally, an \textit{in-situ} calibration method, leveraging the inherent mutual coupling in an array, is proposed as a solution to maintaining a high level of performance in a fielded digital array system over the system's lifetime. The combination of the proposed training waveform and \textit{in-situ} calibration technique prove to be very effective at adaptively creating a generalized solution to extending the dynamic range of future low-cost digital array systems