Spinodal decomposition is a phenomenon involving spontaneous phase separation in a solid alloy. It is often considered as the prototype of second order phase transitions and is known for the formation of non-trivial patterns. In the presence of a lattice mismatch f between the components, even more complex, qualitatively different patterns emerge, depending on the specific f values. Despite being interesting in practical and theoretical settings, modeling this class of phenomena may be hindered by computational costs. Lately, applications of Machine Learning (ML) promise to mitigate these issues. The availability of suitable datasets is therefore of primary importance for the development of said models. We here provide a collection of phase field simulations of spinodal decomposition involving elastic effects under different mismatch conditions f. These may be used in training a ML model both for the forward problem of predicting the evolution given an initial condition and for the inverse problem of extracting the misfit parameter from a sequence. The dataset is conveniently already divided into training, validation and test sets. The data also support the ML framework, based on a convolutional recurrent scheme, discussed in the related publication in refrences and allows for the full reproduction of the reported findings. Once trained, the neural network is able to accurately reproduce ground-truth evolution even in critical regions of the parameter space (e.g., near the onset of metastability) and predict the misfit parameters to a high degree of accuracy (~0.01% absolute strain).

Spinodal decomposition is a phenomenon involving spontaneous phase separation in a solid alloy. It is often considered as the prototype of second order phase transitions and is known for the formation of non-trivial patterns. In the presence of a lattice mismatch f between the components, even more complex, qualitatively different patterns emerge, depending on the specific f values. Despite being interesting in practical and theoretical settings, modeling this class of phenomena may be hindered by computational costs. Lately, applications of Machine Learning (ML) promise to mitigate these issues. The availability of suitable datasets is therefore of primary importance for the development of said models. We here provide a collection of phase field simulations of spinodal decomposition involving elastic effects under different mismatch conditions f. These may be used in training a ML model both for the forward problem of predicting the evolution given an initial condition and for the inverse problem of extracting the misfit parameter from a sequence. The dataset is conveniently already divided into training, validation and test sets. The data also support the ML framework, based on a convolutional recurrent scheme, discussed in the related publication in refrences and allows for the full reproduction of the reported findings. Once trained, the neural network is able to accurately reproduce ground-truth evolution even in critical regions of the parameter space (e.g., near the onset of metastability) and predict the misfit parameters to a high degree of accuracy (~0.01% absolute strain).

Deep Generative models have shown impressive capabilities in several applications, e.g., image, video, and audio synthesis. Importantly, they can infer probability distributions from data implicitly. For this reason, they have promising applications in learning stochastic dynamics, with potential applications in computational condensed matter physics and materials science. Indeed, random thermal fluctuations have a key role in several phenomena, such as surface roughening, nucleation, crystal growth, and phase transitions. Here we provide a comprehensive dataset of trajectories of one of such systems, i.e., the progressive roughening of monoatomic steps on top of a simple cubic (100) surface. The system has been simulated with a Kinetic Monte Carlo approach, implementing the edge diffusion conditions. Among other characteristics, this system is convenient because its dynamics can be represented as a series of binary images, with white and black pixels corresponding to occupied and unoccupied surface sites, respectively. The repository contains 3 KMC datasets composed of 300 independent trajectories each. Every trajectory contains 1000 subsequent states. The datasets differ in the initial condition (one flat stripe and one undulated one on a 64x64 computational cell) and the domain size (one undulated stripe on a 72x64 computational cell). Evolutions predicted by a Generative Adversarial Network approach trained on the flat stripe dataset are also provided, serving as a benchmark for comparing alternative implementations on the same problem. These comprise the evolution of flat profiles on domains of different lengths (32, 48, 64, 72, 80, 96, and 128) to the equilibrium value and relaxation dynamics from undulated profiles conformal to those used in the KMC datasets.

Deep Generative models have shown impressive capabilities in several applications, e.g., image, video, and audio synthesis. Importantly, they can infer probability distributions from data implicitly. For this reason, they have promising applications in learning stochastic dynamics, with potential applications in computational condensed matter physics and materials science. Indeed, random thermal fluctuations have a key role in several phenomena, such as surface roughening, nucleation, crystal growth, and phase transitions. Here we provide a comprehensive dataset of trajectories of one of such systems, i.e., the progressive roughening of monoatomic steps on top of a simple cubic (100) surface. The system has been simulated with a Kinetic Monte Carlo approach, implementing the edge diffusion conditions. Among other characteristics, this system is convenient because its dynamics can be represented as a series of binary images, with white and black pixels corresponding to occupied and unoccupied surface sites, respectively. The repository contains 3 KMC datasets composed of 300 independent trajectories each. Every trajectory contains 1000 subsequent states. The datasets differ in the initial condition (one flat stripe and one undulated one on a 64x64 computational cell) and the domain size (one undulated stripe on a 72x64 computational cell). Evolutions predicted by a Generative Adversarial Network approach trained on the flat stripe dataset are also provided, serving as a benchmark for comparing alternative implementations on the same problem. These comprise the evolution of flat profiles on domains of different lengths (32, 48, 64, 72, 80, 96, and 128) to the equilibrium value and relaxation dynamics from undulated profiles conformal to those used in the KMC datasets.