Physics

There is renewed interest in developing small modular reactors and micro-reactors. Innovation is necessary in both construction and operation methods of these reactors to be financially attractive. For operation, an area of interest is the development of fully autonomous reactor control. Significant efforts are necessary to demonstrate an autonomous control framework for a nuclear system, while adhering to established safety criteria. Our group has proposed and received support for demonstration of an autonomous framework on a subcritical system: the MIT Graphite Exponential Pile. In order to have a fast response (on the order of miliseconds), we must extract specific capabilities of general-purpose system codes to a surrogate model. Thus, we have adopted current state-of-the-art neural network libraries to build surrogate models. This work focuses on establishing the capability of neural networks to provide an accurate and precise multi-dimensional regression of a nuclear reactor's power distribution. We assess using a neural network surrogate against a previously validated model: an MCNP5 model of the MIT reactor. The results indicate that neural networks are an appropriate choice for surrogate models to implement in an autonomous reactor control framework. The MAPE across all test datasets was < 1.16 % with a corresponding standard deviation of < 0.77 %. The error is low, considering that the node-wise fission power can vary from 7 kW to 30 kW across the core.

In this work we study the inverse quantum scattering via deep learning regression, which is implemented via a Multilayer Perceptron. A step-by-step method is provided in order to obtain the potential parameters. A circular boundary-wall potential was chosen to exemplify the method. Detailed discussion about the training is provided. A investigation with noisy data is presented and it is observed that the neural network is useful to predict the potential parameters.

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the formulation and numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depolarization cycle occurring at every heart beat that models the time evolution of the electrical potential across the cell membrane, as well as a set of ionic variables. Multiple solutions of these systems, corresponding to different model inputs, are required to evaluate outputs of clinical interest, such as activation maps and action potential duration. More importantly, these models feature coherent structures that propagate over time, such as wavefronts. These systems can hardly be reduced to lower dimensional problems by conventional reduced order models (ROMs) such as, e.g., the reduced basis (RB) method. This is primarily due to the low regularity of the solution manifold (with respect to the problem parameters) as well as to the nonlinear nature of the input-output maps that we intend to reconstruct numerically. To overcome this difficulty, in this paper we propose a new, nonlinear approach which exploits deep learning (DL) algorithms to obtain accurate and efficient ROMs, whose dimensionality matches the number of system parameters. Our DL approach combines deep feedforward neural networks (NNs) and convolutional autoencoders (AEs). We show that the proposed DL-ROM framework can efficiently provide solutions to parametrized electrophysiology problems, thus enabling multi-scenario analysis in pathological cases. We investigate three challenging test cases in cardiac electrophysiology and prove that DL-ROM outperforms classical projection-based ROMs.

Data assimilation in subsurface flow systems is challenging due to the large number of flow simulations often required, and by the need to preserve geological realism in the calibrated (posterior) models. In this work we present a deep-learning-based surrogate model for two-phase flow in 3D subsurface formations. This surrogate model, a 3D recurrent residual U-Net (referred to as recurrent R-U-Net), consists of 3D convolutional and recurrent (convLSTM) neural networks, designed to capture the spatial-temporal information associated with dynamic subsurface flow systems. A CNN-PCA procedure (convolutional neural network post-processing of principal component analysis) for parameterizing complex 3D geomodels is also described. This approach represents a simplified version of a recently developed supervised-learning-based CNN-PCA framework. The recurrent R-U-Net is trained on the simulated dynamic 3D saturation and pressure fields for a set of random `channelized' geomodels (generated using 3D CNN-PCA). Detailed flow predictions demonstrate that the recurrent R-U-Net surrogate model provides accurate results for dynamic states and well responses for new geological realizations, along with accurate flow statistics for an ensemble of new geomodels. The 3D recurrent R-U-Net and CNN-PCA procedures are then used in combination for a challenging data assimilation problem involving a channelized system. Two different algorithms, namely rejection sampling and an ensemble-based method, are successfully applied. The overall methodology described in this paper may enable the assessment and refinement of data assimilation procedures for a range of realistic and challenging subsurface flow problems.

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard numerical methods can simulate the different regimes quite accurately. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks (NNs). We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. The DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a plug-and-play mode.

We present a method to construct a continuous extension (otherwise known as dense output) for a numerical routine in the special case of the numerical solution being a scalar-valued function exhibiting rapid oscillations. Such cases call for numerical routines that make use of the known global behaviour of the solution, one example being methods using asymptotic expansions to forecast the solution at each step of the independent variable. An example is oscode, numerical routine which uses the Wentzel-Kramers-Brillouin (WKB) approximation when the solution oscillates rapidly and otherwise behaves as a Runge-Kutta (RK) solver. Polynomial interpolation is not suitable for producing the solution at an arbitrary point mid-step, since efficient numerical methods based on the WKB approximation will step through multiple oscillations in a single step. Instead we construct the continuous solution by extending the numerical quadrature used in computing a WKB approximation of the solution with no additional evaluations of the differential equation or terms within, and provide an error estimate on this dense output. Finally, we draw attention to previous work on the continuous extension of Runge-Kutta formulae, and construct an extension to a RK method based on Gauss--Lobatto quadrature nodes, thus describing how to generate dense output from each of the methods underlying oscode.

We perform micromagnetic simulations to study the switching barriers in square artificial spin ice systems consisting of elongated single domain magnetic islands arranged on a square lattice. By considering a double vertex composed of one central island and six nearest neighbor islands, we calculate the energy barriers between two types of double vertices by applying the string method. We investigate by means of micromagnetic simulations the consequences of the neighboring islands, the inhomogeneities in the magnetization of the islands and the reversal mechanisms on the energy barrier by comparing three different approaches with increasing complexity. The micromagnetic models, where the string method is applied, are compared to the currently common method, the mean barrier approximation. Our investigations indicate that a proper micromagnetic modeling of the switching process leads to significantly lower energy barriers, by up to 35% compared to the mean-barrier approximation, so decreasing the expected average life time up to seven orders of magnitude. Hereby, we investigate the influence of parallel switching channels and the conceptional approach of using a mean-barrier to calculate the corresponding rates.

In nanoscale, motion operation of a nano-objective is usually realized by displacement load, which put forwards high requirement for ductility of material. Since pristine graphene has low ductility, once the stretching strain exceeds its critical value, it breaks in brittle style and loses ability to bear the external load quickly. Herein, to improve the ductility, a corrugated sandwich carbon nano-network model based on few-layered graphene is proposed, in which the two surface layers are bonded with several corrugated core layers via benzene molecules. Effects of factors such as the geometry of the carbon network, temperature, and strain rate, on the ductility are evaluated by molecular dynamics simulations. Conclusions are drawn for potential application of the new two-dimensional material with designable ductility.

Abstract Interatomic potentials constitute the key component of large-scale atomistic simulations of materials. The recently proposed physically-informed neural network (PINN) method combines a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential applicable to both metals and nonmetals. In this paper, we present a modified version of the PINN method that accelerates the potential training process and further improves the transferability of PINN potentials to unknown atomic environments. As an application, a modified PINN potential for Al has been developed by training on a large database of electronic structure calculations. The potential reproduces the reference first-principles energies within 2.6 meV per atom and accurately predicts a wide spectrum of physical properties of Al. Such properties include, but are not limited to, lattice dynamics, thermal expansion, energies of point and extended defects, the melting temperature, the structure and dynamic properties of liquid Al, the surface tensions of the liquid surface and the solid-liquid interface, and the nucleation and growth of a grain boundary crack. Computational efficiency of PINN potentials is also discussed.

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented as a function of the elements of a skew-Hermitian matrix that can be optimized directly using unconstrained minimization methods. An implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and a preconditioner is presented and the performance compared with that of the commonly used self-consistent field approach. Results are presented for the G2 set of 148 molecules, liquid water configurations with up to 576 molecules and some insulating crystals. A general preconditioner is presented that is applicable to systems with fractional orbital occupation as is, for example, needed in the k-point sampling for periodic systems. This exponential transformation direct minimization approach is found to outperform the standard implementation of the self-consistent field approach in that all the calculations converge with the same set of parameter values and it requires less computational effort on average. The formulation of the exponential transformation and the gradients of the energy presented here are quite general and can be applied to energy functionals that are not unitary invariant such as self-interaction corrected functionals.