Convolutional Recurrent Neural Networks for tackling materials dynamics at the mesoscale

In the last decade, Machine Learning (ML) has become an essential tool in materials modeling [1]. In particular, Neural Networks (NNs) promise to be able to substitute computationally demanding calculations with fast yet accurate approximations. While this paradigm has proven particularly effective for atomistic simulations [2], applications to continuum models appear to be less common. Yet, also this class of approaches suffers from computational bottlenecks stemming, e.g., from discretization requirements and time-integration schemes. We here show how Convolutional Recurrent NN (CRNN) can be suitably adapted [3,4] to obtain a ML model capable of predicting the mesoscale dynamics of materials based on a suitable dataset of time sequences. In practice, CRNNs manipulate sequences and can be used to directly generate subsequent states in the system dynamics starting from a given initial condition. We notice that CRNN methods are particularly appealing, as they can leverage parallel architectures (e.g. GPUs) and can be generalized to computational domains larger than those observed as training examples. Crucially, NNs are not limited to small time intervals between subsequent states, effectively speeding up sequence generation with respect to traditional integration algorithms. NNs capability of capturing complex, non-linear relationships also alleviates the requirement for fine discretization. For these reasons, this class of approaches is suitable for employment in high throughput workflows and in reaching sizes and timescales difficult to handle with more standard methods. As a first application, we train the CRNN architecture on sequences generated from 2D and 3D phase-field simulations for some prototypical models, such as spinodal decomposition and evolution by surface diffusion. Approximation errors are quantified both in terms of one-to-one correspondence and average properties, comparing the NN predictions with unobserved sequences. Long-term behavior is also discussed, showing under which circumstances the NN prediction is affected by error accumulation and when, instead, it can produce the correct stationary state even if it was not present in the original dataset. [1] P. Mehta et al., A high-bias, low-variance introduction to Machine Learning for physicists, Physics Reports vol. 810 (2019), p. 1-124. [2] M. Hellström et al., Handbook of Materials Modeling: Methods: Theory and Modeling (2020): 661. [3] K. Yang et al., Patterns, vol. 2, no. 5, (2021): 100243. [4] D. Lanzoni, et al., Physical Review Materials 6.10 (2022): 103801.