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Abstract This paper presents the smart distributed data factory (SDDF), an AI-driven distributed computing platform designed to address challenges in drug discovery by creating comprehensive datasets of molecular conformations and their properties. SDDF uses volunteer computing, leveraging the processing power of personal computers worldwide to accelerate quantum chemistry (DFT) calculations. To tackle the vast chemical space and limited high-quality data, SDDF employs an ensemble of machine learning (ML) models to predict molecular properties and selectively choose the most challenging data points for further DFT calculations. The platform also generates new molecular conformations using molecular dynamics with the forces derived from these models. SDDF makes several contributions: the volunteer computing platform for DFT calculations; an active learning framework for constructing a dataset of molecular conformations; a large public dataset of diverse ENAMINE molecules with calculated energies; an ensemble of ML models for accurate energy prediction. The energy dataset was generated to validate the SDDF approach of reducing the need for extensive calculations. With its strict scaffold split, the dataset can be used for training and benchmarking energy models. By combining active learning, distributed computing, and quantum chemistry, SDDF offers a scalable, cost-effective solution for developing accurate molecular models and ultimately accelerating drug discovery.

In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.

Abstract We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a C 0 $C_{0}$ -semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff measure of noncompactness. We justify the scheme of semidiscretization of the Cauchy problem for a differential equation of a given type and evaluate the topological index of the solution set. This makes it possible to obtain a result on the approximation of solutions to the problem.

We obtained results on the existence and uniqueness of a mild solution for a fractional-order semi-linear differential inclusion in a Hilbert space whose right-hand side contains an unbounded linear monotone operator and a Carathéodory-type multivalued nonlinearity satisfying some monotonicity condition in the phase variables. We used the Yosida approximations of the linear part of the inclusion, the method of a priori estimates of solutions, and the topological degree method for condensing vector fields. As an example, we considered the existence and uniqueness of a solution to the Cauchy problem for a system governed by a perturbed subdifferential inclusion of a fractional diffusion type.