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Abstract In this work, we develop a deep neural network model for the reaction rate of oxidative coupling of methane from published high-throughput experimental catalysis data. A neural network is formulated so that the rate model satisfies the plug flow reactor design equation. The model is then employed to understand the variation of reactant and product composition within the reactor for the reference catalyst Mn–Na₂WO₄/SiO₂at different temperatures and to identify new catalysts and combinations of known catalysts that would increase yield and selectivity relative to the reference catalyst. The model revealed that methane is converted in the first half of the catalyst bed, while the second part largely consolidates the products (i.e. increases ethylene to ethane ratio). A screening study of $⩾3400$combinations of pairs of previously studied catalysts of the form M1(M2) ${}_{1-2}$M3O_x/support (where M1, M2 and M3 are metals) revealed that a reactor configuration comprising two sequential catalyst beds leads to synergistic effects resulting in increased yield of C₂compared to the reference catalyst at identical conditions and contact time. Finally, an expanded screening study of 7400 combinations (comprising previously studied metals but with several new permutations) revealed multiple catalyst choices with enhanced yields of C₂products. This study demonstrates the value of learning a deep neural network model for the instantaneous reaction rate directly from high-throughput data and represents a first step in constraining a data-driven reaction model to satisfy domain information. 

Abstract In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first investigate necessary and sufficient conditions for the sketch sampling to have well-defined algorithms. Based on these sampling conditions we develop new sketch descent methods for solving general smooth linearly constrained problems, in particular, random sketch descent (RSD) and accelerated random sketch descent (A-RSD) methods. To our knowledge, this is the first convergence analysis of RSD algorithms for optimization problems with multiple non-separable linear constraints. For the general case, when the objective function is smooth and non-convex, we prove for the non-accelerated variant sublinear rate in expectation for an appropriate optimality measure. In the smooth convex case, we derive for both algorithms, non-accelerated and A-RSD, sublinear convergence rates in the expected values of the objective function. Additionally, if the objective function satisfies a strong convexity type condition, both algorithms converge linearly in expectation. In special cases, where complexity bounds are known for some particular sketching algorithms, such as coordinate descent methods for optimization problems with a single linear coupled constraint, our theory recovers the best known bounds. Finally, we present several numerical examples to illustrate the performances of our new algorithms.