Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian Process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schr\"odinger and Burgers' equations.

Abstract: This paper demonstrates emergence of computational creativity in the field of music. Different aspects of creativity such as producer, process, product and press are studied and formulated. Different notions of computational creativity such as novelty, quality and typicality of compositions as products are studied and evaluated. We formulate an algorithmic perception on human creativity and propose a prototype that is capable of demonstrating human-level creativity. We then validate the proposed prototype by applying various creativity benchmarks with the results obtained and compare the proposed prototype with the other existing computational creative systems. I. INTRODUCTION Computational creativity is the modeling or replicating human creativity computationally. Traditionally computational creativity has focused more on creative systems' products or processes, though this focus has widened recently. Research on creativity offers four Ps of creativity (Rhodes, 1961; MacKinnon, 1970; Jordanous, 2016). These four P's are: 1. Person/Producer: a creative agent 2. Process: an activity done by the creative agent 3. Product: the product of the creative process 4. Press/Environment: the overall environment of creativity 110 The proposed methodology addresses all the four P's of creativity unlike most of recent works, which focus on these individually (Saunders, 2012; Gervas & Leon, 2014; Misztal & Indurkhya, 2014; Sosa & Gero, 2015; Besold & Plaza, 2015; Harmon, 2015). Figure 1 gives a simplified view of proposed computational creative system in the context of four P's of creativity.

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