The recent developments in data-driven methods have paved the way to new methodologies to provide accurate state reconstruction of engineering systems; nuclear reactors represent particularly challenging applications for this task due to the complexity of the strongly coupled physics involved and the extremely harsh and hostile environments, especially for new technologies such as Generation-IV reactors. Data-driven techniques can combine different sources of information, including computational proxy models and local noisy measurements on the system, to robustly estimate the state. This work leverages the novel Shallow Recurrent Decoder architecture to infer the entire state vector (including neutron fluxes, precursors concentrations, temperature, pressure and velocity) of a reactor from three out-of-core time-series neutron flux measurements alone. In particular, this work extends the standard architecture to treat parametric time-series data, ensuring the possibility of investigating different accidental scenarios and showing the capabilities of this approach to provide an accurate state estimation in various operating conditions. This paper considers as a test case the Molten Salt Fast Reactor (MSFR), a Generation-IV reactor concept, characterised by strong coupling between the neutronics and the thermal hydraulics due to the liquid nature of the fuel. The promising results of this work are further strengthened by the possibility of quantifying the uncertainty associated with the state estimation, due to the considerably low training cost. The accurate reconstruction of every characteristic field in real-time makes this approach suitable for monitoring and control purposes in the framework of a reactor digital twin.
Shallow Recurrent Decoder networks are a novel data-driven methodology able to provide accurate state estimation in engineering systems, such as nuclear reactors. This deep learning architecture is a robust technique designed to map the temporal trajectories of a few sparse measures to the full state space, including unobservable fields, which is agnostic to sensor positions and able to handle noisy data through an ensemble strategy, leveraging the short training times and without the need for hyperparameter tuning. The architecture was successfully applied to the Molten Salt Fast Reactor concept; now, this work considers the performance of Shallow Recurrent Decoders on a deployed reactor concept. The underlying model is represented by a fluid dynamics model of the TRIGA Mark II research reactor; the architecture will use both synthetic temperature data coming from the numerical model and leveraging experimental temperature data recorded during a previous campaign. The objectives of this work are therefore: 1) presenting the first application of SHRED to a deployed nuclear reactor (TRIGA Mark II); 2) the integration of hybrid synthetic/experimental data within the SHRED framework; 3) a systematic assessment of SHRED robustness under physically constrained, low-dynamics sensor locations; and 4) a quantitative evaluation of SHRED self-correction capability when model-to-data discrepancies are present. Indeed, this approach is capable of accurately reconstruct every field of interest in real-time, using both synthetic (with an average relative error lower than 4% in euclidean norm) and experimental data (with a RMSE of 1.52 K on the temperature, compared of 1.85 K of the CFD), making it suitable for interpretable monitoring and control purposes in the context of building digital twins for nuclear reactors.
This paper is the second part of the study initiated in [1] and is devoted to finite-time blow-up and global existence for a semilinear heat equation on infinite weighted graphs. We first establish basic results on mild and classical solutions (which, to the best of our knowledge, were not previously available in the setting of graphs) proving their equivalence under suitable assumptions and showing the existence of a solution between a given sub-and supersolution. We then analyze blow-up and global existence on 7LN, providing proofs based on methods different from those used on 7LN in the existing literature. Moreover, for graphs with positive spectral gap, we prove global existence for small initial data. In contrast with previous functional analytic approaches yielding mild solutions, our method relies on the construction of global-in-time supersolutions and leads to the existence of classical solutions.
Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs projects the high-dimensional full-order model (FOM) dynamics onto a low-dimensional manifold. These projection-based ROMs approaches often rely on classical model reduction techniques such as proper orthogonal decomposition (POD) or, more recently, on neural network architectures such as autoencoders (AEs). In the case that the ROM is constructed by the POD, one has approximation guaranteed based on the singular values of the problem at hand. However, POD-based techniques can suffer from slow decay of the singular values in transport-and advection-dominated problems. In contrast to that, AEs allow for better reduction capabilities than the POD, often with the first few modes, but at the price of theoretical considerations. In addition, it is often observed, that AEs exhibits a plateau of the projection error with the increment of the dimension of the trial manifold. In this work, we propose a deep invertible AE architecture, named inv-AE, that computationally improves upon the stagnation of the reconstruction error typical of traditional AE architectures, e.g., convolutional, and the reconstructions quality. Inv-AE is composed of several invertible neural network layers that allows for gradually recovering more information about the FOM solutions the more we increase the dimension of the reduced manifold. Through the application of inv-AE to a parametric 1dimensional Burgers' equation, a parametric 2-dimensional fluid flow around an obstacle with variable geometry, and a parametric 3-dimensional Korteweg-de Vries, we show that (i) inv-AE mitigates the issue of the characteristic plateau of (convolutional and fully connected) AEs and (ii) inv-AE can be combined with popular autoencoder-based ROM approaches, e.g., DL-ROM and POD-DL-ROM, to improve their accuracy.
Deploying deep neural networks (DNNs) on power-sensitive edge devices presents a formidable challenge. While Dynamic Voltage and Frequency Scaling (DVFS) is widely employed for energy optimization, traditional model-level scaling is often too coarse to capture intra-inference variations, whereas fine-grained operator-level scaling suffers from prohibitive performance degradation due to significant hardware switching latency. This paper presents SparseDVFS, a fine-grained, sparse-aware DVFS framework designed for energy-efficient edge inference. Our key insight is that operator sparsity is a primary metric for hardware frequency modulation. By distinguishing between compute-bound dense operators and memory-bound sparse operators, the system can apply specialized frequency triplets to maximize energy efficiency. To overcome switching overheads and component interference, SparseDVFS incorporates three key innovations: (1) an offline modeler that established a deterministic mapping between operator sparsity and optimal frequency triplets (CPU/GPU/EMC) via white-box timeline analysis; (2) a runtime graph partitioner that utilizes a greedy merging heuristic to aggregate operators into super-blocks, balancing scaling granularity and DVFS switching latency through a latency amortization constraint; and (3) a unified co-governor that employs a frequency unified scaling engine (FUSE) and a look-ahead instruction queue to eliminate antagonistic effects between independent controllers and hide hardware transition latencies. Extensive evaluations show that SparseDVFS achieves an average 78.17
