The reservoir computer comprises a reservoir of possibly non-linear, possibly chaotic dynamics. By perturbing and taking outputs from this reservoir, its dynamics may be harnessed to compute complex problems at “the edge of chaos”. One of the first forms of reservoir computer, the Echo State Network (ESN), is a form of artificial neural network that builds its reservoir from a large and sparsely connected recurrent neural network (RNN). The ESN was initially introduced as an innovative solution to train RNNs which, up until that point, was a notoriously difficult task. The innovation of the ESN is that, rather than train the RNN weights, only the output is trained. If this output is assumed to be linear, then linear regression may be used. This work presents an effort to implement the Echo State Network, and an offline linear regression training method based on Tikhonov regularisation. This implementation targeted the general purpose graphics processing unit (GPU or GPGPU). The behaviour of the implementation was examined by comparing it with a central processing unit (CPU) implementation, and by assessing its performance against several studied learning problems. These assessments were performed using all 4 cores of the Intel i7-980 CPU and an Nvidia GTX480. When compared with a CPU implementation, the GPU ESN implementation demonstrated a speed-up starting from a reservoir size of between 512 and 1,024. A maximum speed-up of approximately 6 was observed at the largest reservoir size tested (2,048). The Tikhonov regularisation (TR) implementation was also compared with a CPU implementation. Unlike the ESN execution, the GPU TR implementation was largely slower than the CPU implementation. Speed-ups were observed at the largest reservoir and state history sizes, the largest of which was 2.6813. The learning behaviour of the GPU ESN was tested on three problems, a sinusoid, a Mackey-Glass time-series, and a multiple superimposed oscillator (MSO). The normalised root-mean squared errors of the predictors were compared. The best observed sinusoid predictor outperformed the best MSO predictor by 4 orders of magnitude. In turn, the best observed MSO predictor outperformed the best Mackey-Glass predictor by 2 orders of magnitude.

Pass-by noise testing is an important step in vehicle design and regulation compliance. Finite element analysis simulations have been used to cut costs on prototyping and testing, but the high computational cost of simulating surface vibrations from complex geometries and the resulting airborne noise propagation is making the switch to digital twin methods not viable. This paper aims at investigating the use of equivalent source methods as an alternative to the before mentioned simulations. Through the use of a simple 2D model, the difficulties such as ill-conditioning of the transfer matrix and the required regularisation techniques such as TSVD and the Tikhonov L-curve method are tested and then applied to a mesh of a 3D engine model. Source and pressure field errors are measured and their origins are explained. A heavy emphasis is put on the model geometry as a source of error. Finally, rules of thumb based on the regularisation balance and the wavelength dependent pressure sampling positions are formulated in order to achieve usable results. / Bullerprovning vid passage är ett viktigt steg i fordonsdesign och regelefterlevnad. Simuleringar med finita elementanalyser har använts för att minska kostnaderna för prototypframtagning och provning, men de höga beräkningskostnaderna för att simulera ytvibrationer från komplexa geometrier och den resulterande luftburna bullerspridningen gör att övergången till digitala tvillingmetoder inte är genomförbar. Denna uppsats syftar till att undersöka användningen av ekvivalenta källmetoder som ett alternativ till de tidigare nämnda simuleringarna. Genom att använda en enkel 2D-modell testas svårigheterna som dålig konditionering av överföringsmatrisen och de nödvändiga regulariseringsteknikerna som TSVD och Tikhonov L-kurvmetoden och tillämpas sedan på ett nät av en 3D-motormodell. Käll- och tryckfältsfel mäts och deras ursprung förklaras. Stor vikt läggs vid modellgeometrin som en felkälla. Slutligen formuleras tumregler baserade på regulariseringsbalansen och de våglängdsberoende tryckprovtagningspositionerna för att uppnå användbara resultat.