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Register a new userScale bridging materials physics: Active learning workflows and integrable deep neural networks for free energy function representations in alloys
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The free energy plays a fundamental role in descriptions of many systems in continuum physics. Notably, in multiphysics applications, it encodes thermodynamic coupling between different fields. It thereby gives rise to driving forces on the dynamics of interaction between the constituent phenomena. In mechano-chemically interacting materials systems, even consideration of only compositions, order parameters and strains can render the free energy to be reasonably high-dimensional. In proposing the free energy as a paradigm for scale bridging, we have previously exploited neural networks for their representation of such high-dimensional functions. Specifically, we have developed an integrable deep neural network (IDNN) that can be trained to free energy derivative data obtained from atomic scale models and statistical mechanics, then analytically integrated to recover a free energy density function. The motivation comes from the statistical mechanics formalism, in which certain free energy derivatives are accessible for control of the system, rather than the free energy itself. Our current work combines the IDNN with an active learning workflow to improve sampling of the free energy derivative data in a high-dimensional input space. Treated as input-output maps, machine learning accommodates role reversals between independent and dependent quantities as the mathematical descriptions change with scale bridging. As a prototypical system we focus on Ni-Al. Phase field simulations using the resulting IDNN representation for the free energy density of Ni-Al demonstrate that the appropriate physics of the material have been learned. To the best of our knowledge, this represents the most complete treatment of scale bridging, using the free energy for a practical materials system, that starts with electronic structure calculations and proceeds through statistical mechanics to continuum physics.
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Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs surrogate modeling for turbulent Rayleigh-B{e}nard (RB) convection flows in rough and smooth rectangular cavities, mainly relying on DNS temperature data from the fluid bulk. We carefully quantify the computational requirements under which the formulation is capable of accurately recovering the flow hidden quantities. We then propose a new padding technique to distribute some of the scattered coordinates-at which PDE residuals are minimized-around the region of labeled data acquisition. We show how it comes to play as a regularization close to the training boundaries which are zones of poor accuracy for standard PINNs and results in a noticeable global accuracy improvement at iso-budget. Finally, we propose for the first time to relax the incompressibility condition in such a way that it drastically benefits the optimization search and results in a much improved convergence of the composite loss function. The RB results obtained at high Rayleigh number Ra = 2 $bullet$ 10 9 are particularly impressive: the predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [0.3% -- 4%] in the relative L 2 norm, with a training relying only on 1.6% of the DNS data points.
This digital book contains a practical and comprehensive introduction of everything related to deep learning in the context of physical simulations. As much as possible, all topics come with hands-on code examples in the form of Jupyter notebooks to quickly get started. Beyond standard supervised learning from data, well look at physical loss constraints, more tightly coupled learning algorithms with differentiable simulations, as well as reinforcement learning and uncertainty modeling. We live in exciting times: these methods have a huge potential to fundamentally change what computer simulations can achieve.
With ever-increasing computational demand for deep learning, it is critical to investigate the implications of the numeric representation and precision of DNN model weights and activations on computational efficiency. In this work, we explore unconventional narrow-precision floating-point representations as it relates to inference accuracy and efficiency to steer the improved design of future DNN platforms. We show that inference using these custom numeric representations on production-grade DNNs, including GoogLeNet and VGG, achieves an average speedup of 7.6x with less than 1% degradation in inference accuracy relative to a state-of-the-art baseline platform representing the most sophisticated hardware using single-precision floating point. To facilitate the use of such customized precision, we also present a novel technique that drastically reduces the time required to derive the optimal precision configuration.
Graph neural networks (GNNs) integrate deep architectures and topological structure modeling in an effective way. However, the performance of existing GNNs would decrease significantly when they stack many layers, because of the over-smoothing issue. Node embeddings tend to converge to similar vectors when GNNs keep recursively aggregating the representations of neighbors. To enable deep GNNs, several methods have been explored recently. But they are developed from either techniques in convolutional neural networks or heuristic strategies. There is no generalizable and theoretical principle to guide the design of deep GNNs. To this end, we analyze the bottleneck of deep GNNs by leveraging the Dirichlet energy of node embeddings, and propose a generalizable principle to guide the training of deep GNNs. Based on it, a novel deep GNN framework -- EGNN is designed. It could provide lower and upper constraints in terms of Dirichlet energy at each layer to avoid over-smoothing. Experimental results demonstrate that EGNN achieves state-of-the-art performance by using deep layers.
Recent advances in deep learning have made available large, powerful convolutional neural networks (CNN) with state-of-the-art performance in several real-world applications. Unfortunately, these large-sized models have millions of parameters, thus they are not deployable on resource-limited platforms (e.g. where RAM is limited). Compression of CNNs thereby becomes a critical problem to achieve memory-efficient and possibly computationally faster model representations. In this paper, we investigate the impact of lossy compression of CNNs by weight pruning and quantization, and lossless weight matrix representations based on source coding. We tested several combinations of these techniques on four benchmark datasets for classification and regression problems, achieving compression rates up to $165$ times, while preserving or improving the model performance.
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