Deep residual error and bag-of-tricks learning for gravitational wave surrogate modeling

Accelerating multimodal gravitational waveforms from precessing compact binaries with artificial neural networks

“…In this work we combine reduced-order modeling with the power of artificial neural networks (ANNs) to build a computationally vastly more efficient surrogate model of the state-of-the-art IMR waveform model SEOBNR4PHM [30] that includes both spin-induced orbital precession [31] and higher-order modes beyond the quadrupole emission. While the efficacy of this approach has previously been demonstrated for the quadrupole [(2,2)-] mode of aligned-spin binary black holes (BBHs) [19,32], here we demonstrate its feasibility for the multimodal, precessing case. To achieve this, we decompose the SEOBNR4PHM waveform model into eight components that describe the modes in a noninertial, coprecessing coordinate frame and three components that encode the precession dynamics.…”

“…Therefore, their range of validity in parameter space is limited to the region over which they are constructed, the training space, plus an extrapolation region over which the model has been tested and shown to be accurate to within some tolerance. Recent examples of surrogate models for waveforms from coalescing compact binaries include numerical relativity (NR) and NR-hybrid surrogate models [13,14,16,[33][34][35], surrogates for the aligned-spin effectiveone-body (EOB) model SEOBNRv4 [36] using artificial neural networks [19,32], and a machine learning emulation of a different EOB model, TEOBResumS [37,38].…”

“…where A i and ϕ i are the amplitude and phase at the ith empirical node. The 2n functions that determine the parameter space fits can be determined by different means, for example via traditional fitting functions such as splines or polynomials [10,13,16] or by using machine learning algorithms such artificial neural networks [19,32] or Gaussian processes [33,34,41,42]. In this work, we will follow Ref.…”

“…The package then creates and trains neural networks with hyperparameters drawn from these choices, and returns the best performing hyperparameters based on a metric, which we specify to be the validation loss upon completion of training. The choices for optimizable hyperparameters are as follows: activation function (Relu [63,64], Elu [65], Tanh, SOFTMAX, SOFTPLUS, SOFTSIGN [66]), optimizer (ADAM [67], NADAM [68], ADAMAX [67], ADADELTA [69]), number of training epochs (1000, 2000, 10,000), and minibatch size (32,64,128). We refer the reader to [70] for a systematic overview of activation functions and [71] for an overview of gradient descent optimization algorithms.…”

“…In addition to the default network above, we also constructed a neural network for the residuals between the input empirical interpolation coefficients and the default neural network predictions (see also [32]), ỹk ¼ y true k − y pred k . This allows us to reconstruct the empirical interpolation coefficients using a two-step procedure: We first evaluate the default neural network then we correct for any residual errors using the second network.…”