arXiv subjects

Daniele Lanzoni

Publications and source records attributed to Daniele Lanzoni.

7 recordsLinked to original sources

arXiv2026

Neural surrogates for crystal growth dynamics with variable supersaturation: explicit vs. implicit conditioning

Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.

cond-mat.mtrl-sci↗

arXiv2025

Unified machine-learning framework for property prediction and time-evolution simulation of strained alloy microstructure

We introduce a unified machine-learning framework designed to conveniently tackle the temporal evolution of alloy microstructures under the influence of an elastic field. This approach allows for the simultaneous extraction of elastic parameters from a short trajectory and for the prediction of further microstructure evolution under their influence. This is demonstrated by focusing on spinodal decomposition in the presence of a lattice mismatch eta, and by carrying out an extensive comparison between the ground-truth evolution supplied by phase field simulations and the predictions of suitable convolutional recurrent neural network architectures. The two tasks may then be performed subsequently into a cascade framework. Under a wide spectrum of misfit conditions, the here-presented cascade model accurately predicts eta and the full corresponding microstructure evolution, also when approaching critical conditions for spinodal decomposition. Scalability to larger computational domain sizes and mild extrapolation errors in time (for time sequences five times longer than the sampled ones during training) are demonstrated. The proposed framework is general and can be applied beyond the specific, prototypical system considered here as an example. Intriguingly, experimental videos could be used to infer unknown external parameters, prior to simulating further temporal evolution.

cond-mat.mtrl-sci↗

arXiv2025

Learning Kinetic Monte Carlo stochastic dynamics with Deep Generative Adversarial Networks

We show that Generative Adversarial Networks (GANs) may be fruitfully exploited to learn stochastic dynamics, surrogating traditional models while capturing thermal fluctuations. Specifically, we showcase the application to a two-dimensional, many-particle system, focusing on surface-step fluctuations and on the related time-dependent roughness. After the construction of a dataset based on Kinetic Monte Carlo simulations, a conditional GAN is trained to propagate stochastically the state of the system in time, allowing the generation of new sequences with a reduced computational cost. Modifications with respect to standard GANs, which facilitate convergence and increase accuracy, are discussed. The trained network is demonstrated to quantitatively reproduce equilibrium and kinetic properties, including scaling laws, with deviations of a few percent from the exact value. Extrapolation limits and future perspectives are critically discussed.

cond-mat.stat-mech↗

arXiv2024

Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired Neural Networks for the 3D microstructure evolution of materials via Cahn-Hilliard flow

A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn-Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the Free energy is also demonstrated up to the late coarsening stages, proving that this class of Machine Learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.

cond-mat.mes-hall↗

arXiv2024

Quantitative analysis of the prediction performance of a Convolutional Neural Network evaluating the surface elastic energy of a strained film

A Deep Learning approach is devised to estimate the elastic energy density $ρ$ at the free surface of an undulated stressed film. About 190000 arbitrary surface profiles h(x) are randomly generated by Perlin noise and paired with the corresponding elastic energy density profiles $ρ(x)$, computed by a semi-analytical Green's function approximation, suitable for small-slope morphologies. The resulting dataset and smaller subsets of it are used for the training of a Fully Convolutional Neural Network. The trained models are shown to return quantitative predictions of $ρ$, not only in terms of convergence of the loss function during training, but also in validation and testing, with better results in the case of the larger dataset. Extensive tests are performed to assess the generalization capability of the Neural Network model when applied to profiles with localized features or assigned geometries not included in the original dataset. Moreover, its possible exploitation on domain sizes beyond the one used in the training is also analyzed in-depth. The conditions providing a one-to-one reproduction of the ground-truth $ρ(x)$ profiles computed by the Green's approximation are highlighted along with critical cases. The accuracy and robustness of the deep-learned $ρ(x)$ are further demonstrated in the time-integration of surface evolution problems described by simple partial differential equations of evaporation/condensation and surface diffusion.

physics.comp-ph↗

arXiv2023

Accurate generation of stochastic dynamics based on multi-model Generative Adversarial Networks

Generative Adversarial Networks (GANs) have shown immense potential in fields such as text and image generation. Only very recently attempts to exploit GANs to statistical-mechanics models have been reported. Here we quantitatively test this approach by applying it to a prototypical stochastic process on a lattice. By suitably adding noise to the original data we succeed in bringing both the Generator and the Discriminator loss functions close to their ideal value. Importantly, the discreteness of the model is retained despite the noise. As typical for adversarial approaches, oscillations around the convergence limit persist also at large epochs. This undermines model selection and the quality of the generated trajectories. We demonstrate that a simple multi-model procedure where stochastic trajectories are advanced at each step upon randomly selecting a Generator leads to a remarkable increase in accuracy. This is illustrated by quantitative analysis of both the predicted equilibrium probability distribution and of the escape-time distribution. Based on the reported findings, we believe that GANs are a promising tool to tackle complex statistical dynamics by machine learning techniques

cond-mat.stat-mech↗

arXiv2022

Morphological evolution via surface diffusion learned by convolutional, recurrent neural networks: extrapolation and prediction uncertainty

We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only relatively simple, isolated shapes. After proper data augmentation, training and validation, the model is shown to correctly predict also the evolution of previously unobserved morphologies and to have learned the correct scaling of the evolution time with size. Importantly, we quantify prediction uncertainties based on a bootstrap-aggregation procedure. The latter proved to be fundamental in pointing out high uncertainties when applying the model to more complex initial conditions (e.g. leading to splitting of high aspect-ratio individual structures). Automatic smart-augmentation of the training set and design of a hybrid simulation method are discussed.

physics.comp-ph↗