| Abstract: |
Dynamic scaling is observed in various natural processes such as circular cell growth, space-time precipitation fields, and landscape evolution. However, predicting the dynamics and capturing the scaling features associated with such stochastic processes remain a grand challenge. In this proposal, we aim to investigate the skill of deep learning strategies in capturing the dynamic scaling of growing interfaces from numerical data. Specifically, a non-linear Langevin-type (Kardar-Parisi-Zhang or KPZ) equation in (1+1) dimensions ∂_t h=ν∂_x^2 h+λ(∂_x h)^2+ξ, exhibiting double scaling relation in space and time will serve as a model test for event prediction. Here, h(x,t) represents the height of the surface from a flat substrate (or the radial distance from the center of the cluster), ν and λ are model parameters, and ξ(x,t) is white noise. We will then use Eden and single-step solid-on-solid models for growth in circular and flat shapes, respectively, to generate numerical solutions and provide training and validating datasets for our neural network. The key research question is whether deep convolutional neural network (DCNN) can be trained to learn the hidden complex structures and scaling properties in random, highly non-linear processes purely from data. Our main goal is to capture accurately the double scaling laws embedded in the numerical datasets.
To achieve this goal, we will adopt the mixed-scale densely connected convolution neural network (MSD-Net) model to capture the scaling properties appearing in the circular cell growth and surface height numerical solutions of the above KPZ equation. To demonstrate that MSD-Net can really capture the dynamics and scaling laws of the processes, we will train and test our network at different system sizes that are expected to exhibit different cross-over (saturation) time. The network will also be tested at several depths (numbers of dense layers used) for accuracy sensitivity. Unlike traditional DCNN, the MSD-Net requires relatively few numbers of training parameters and provides much more computational efficiency for difficult problems. Our code is written in Python language that uses pytorch deep learning library (https://pytorch.org/) and is capable of utilizing multi-GPU, CUDA-based parallel computing framework to significantly reduce the computational time. During the Startup phase, our proposed network will be tested only for small system sizes in space and short timescale. If successful, we will expand this work to larger scales and more complex processes for the next steps. Therefore, we request a Startup account allocation for 2500 node-hours in the AI-GPU nodes of the PSC Bridges system with multiple NVIDIA Volta V100 devices to develop and train our network model. |
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