We present a differentiable extension of the VEROS ocean model, enabling automatic differentiation through its dynamical core. We describe the key modifications required to make the model fully compatible with JAX autodifferentiation framework and evaluate the numerical consistency of the resulting implementation. Two illustrative applications are then demonstrated: (i) the correction of an initial ocean state through gradient-based optimization, and (ii) the calibration of unknown physical parameters directly from model observations. These examples highlight how differentiable programming can facilitate end-to-end learning and parameter tuning in ocean modeling. Our implementation is available online.

Proactive maintenance strategies, such as Predictive Maintenance (PdM), play an important role in the operation of Nuclear Power Plants (NPPs), particularly due to their capacity to reduce offline time by preventing unexpected shutdowns caused by component failures. In this work, we explore the use of a Convolutional Neural Network (CNN) architecture combined with a computational thermomechanical model to calculate the temperature, stress, and strain of a Pressurized Water Reactor (PWR) fuel rod during operation. This estimation relies on a limited number of temperature measurements from the cladding's outer surface. This methodology can potentially aid in developing PdM tools for nuclear reactors by enabling real-time monitoring of such systems. The training, validation, and testing datasets were generated through coupled simulations involving BISON, a finite element-based nuclear fuel performance code, and the MOOSE Thermal-Hydraulics Module (MOOSE-THM). We conducted eleven simulations, varying the peak linear heat generation rates. Of these, eight were used for training, two for validation, and one for testing. The CNN was trained for over 1,000 epochs without signs of overfitting, achieving highly accurate temperature distribution predictions. These were then used in a thermomechanical model to determine the stress and strain distribution within the fuel rod.

Flow boiling plays an important role in enhancing the performance of thermal management systems, including refrigeration, microelectronics cooling, nuclear power plants, and nuclear fission reactors [1, 2]. This phenomenon involves a fluid absorbing heat and undergoing a phase change from liquid to vapor, while supplied with the advection of the bulk flow, significantly boosting the heat transfer efficiency through the utilization of latent heat. The initiation of the phase change is known as the onset of nucleate boiling (ONB) [3]. However, when the liquid fails to rewet the surface, the surface becomes entirely covered by a vapor layer, leading to a significant reduction in heat transfer efficiency. This phenomenon is known as the departure from nucleate boiling (DNB) [4]. The heat transfer process between the ONB and the DNB points can be described using the RPI wall boiling model [5].

This study presents a novel approach for quantificationally reconstructing density fields from shadowgraph images using physics-informed neural networks. The proposed method utilizes the shadowgraph technique visualizing the flow field, enabling reliable quantitative measurement of flow density fields. Compare to traditional methods, which obtain the distribution of physical quality in spatial coordinates case by case. We establish a new end-to-end network that directly from shadowgraph images to physical fields. Besides, the model employs a self-supervised learning approach, without any labeled data. Experimental validations across hot air jets, thermal plumes, and alcohol burner flames prove the model's accuracy and universality. This approach offers a non-invasive, real-time surrogate model for flow diagnostics. It is believed that this technique could cover and become a reliable tool in various scientific and engineering disciplines.

Perceiving the global field from sparse sensors has been a grand challenge in the monitoring, analysis, and design of physical systems. In this context, sensor placement optimization is a crucial issue. Most existing works require large and sufficient data to construct data-based criteria, which are intractable in data-free scenarios without numerical and experimental data. To this end, we propose a novel physics-driven sensor placement optimization (PSPO) method for temperature field reconstruction using a physics-based criterion to optimize sensor locations. In our methodological framework, we firstly derive the theoretical upper and lower bounds of the reconstruction error under noise scenarios by analyzing the optimal solution, proving that error bounds correlate with the condition number determined by sensor locations. Furthermore, the condition number, as the physics-based criterion, is used to optimize sensor locations by the genetic algorithm. Finally, the best sensors are validated by reconstruction models, including non-invasive end-to-end models, non-invasive reduced-order models, and physics-informed models. Experimental results, both on a numerical and an application case, demonstrate that the PSPO method significantly outperforms random and uniform selection methods, improving the reconstruction accuracy by nearly an order of magnitude. Moreover, the PSPO method can achieve comparable reconstruction accuracy to the existing data-driven placement optimization methods.

We propose the Artificial Intelligence Velocimetry-Thermometry (AIVT) method to infer hidden temperature fields from experimental turbulent velocity data. This physics-informed machine learning method enables us to infer continuous temperature fields using only sparse velocity data, hence eliminating the need for direct temperature measurements. Specifically, AIVT is based on physics-informed Kolmogorov-Arnold Networks (not neural networks) and is trained by optimizing a combined loss function that minimizes the residuals of the velocity data, boundary conditions, and the governing equations. We apply AIVT to a unique set of experimental volumetric and simultaneous temperature and velocity data of Rayleigh-B\'enard convection (RBC) that we acquired by combining Particle Image Thermometry and Lagrangian Particle Tracking. This allows us to compare AIVT predictions and measurements directly. We demonstrate that we can reconstruct and infer continuous and instantaneous velocity and temperature fields from sparse experimental data at a fidelity comparable to direct numerical simulations (DNS) of turbulence. This, in turn, enables us to compute important quantities for quantifying turbulence, such as fluctuations, viscous and thermal dissipation, and QR distribution. This paradigm shift in processing experimental data using AIVT to infer turbulent fields at DNS-level fidelity is a promising avenue in breaking the current deadlock of quantitative understanding of turbulence at high Reynolds numbers, where DNS is computationally infeasible.

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function inspired by the finite element method (FEM) with the implicit Euler time integration scheme. A transient thermal conduction problem is considered to benchmark the performance. The proposed operator learning framework takes a temperature field at the current time step as input and predicts a temperature field at the next time step. The Galerkin discretized weak formulation of the heat equation is employed to incorporate physics into the loss function, which is coined finite operator learning (FOL). Upon training, the networks successfully predict the temperature evolution over time for any initial temperature field at high accuracy compared to the FEM solution. The framework is also confirmed to be applicable to a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for a large data set prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Second, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation when optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry can be handled with FOL, which is crucial to addressing various engineering application scenarios.

A digital twin (DT), with the components of a physics-based model, a data-driven model, and a machine learning (ML) enabled efficient surrogate, behaves as a virtual twin of the real-world physical process. In terms of Laser Powder Bed Fusion (L-PBF) based additive manufacturing (AM), a DT can predict the current and future states of the melt pool and the resulting defects corresponding to the input laser parameters, evolve itself by assimilating in-situ sensor data, and optimize the laser parameters to mitigate defect formation. In this paper, we present a deep neural operator enabled computational framework of the DT for closed-loop feedback control of the L-PBF process. This is accomplished by building a high-fidelity computational model to accurately represent the melt pool states, an efficient surrogate model to approximate the melt pool solution field, followed by an physics-based procedure to extract information from the computed melt pool simulation that can further be correlated to the defect quantities of interest (e.g., surface roughness). In particular, we leverage the data generated from the high-fidelity physics-based model and train a series of Fourier neural operator (FNO) based ML models to effectively learn the relation between the input laser parameters and the corresponding full temperature field of the melt pool. Subsequently, a set of physics-informed variables such as the melt pool dimensions and the peak temperature can be extracted to compute the resulting defects. An optimization algorithm is then exercised to control laser input and minimize defects. On the other hand, the constructed DT can also evolve with the physical twin via offline finetuning and online material calibration. Finally, a probabilistic framework is adopted for uncertainty quantification. The developed DT is envisioned to guide the AM process and facilitate high-quality manufacturing.

However, due to intensive computational requirements, it is not feasible to deploy these techniques directly in numerous cases, such as parametric optimization, real-time prediction for control applications, etc. Machine learning-based surrogate models offer an alternate way for simulation of the physical systems in an efficient manner. Deep learning, due to its ability to model any arbitrary input-output relationship in an efficient manner is the most accepted choice for surrogate modelling. In general, these surrogate models are data driven models, where the simulation/experimental data is used for the training purpose. Once the surrogate model is trained, it can be used to predict the system output for unobserved data with minimal computational effort. For surrogate modelling, both vanilla and specialized neural networks such as convolution neural networks have gained immense popularity in both scientific as well as for industrial applications [1, 2]. Further, recently in [3], operator learning, a new paradigm in deep learning is proposed. In literature, various operator learning techniques are proposed, like deep operator networks (DeepONets)[4], Laplace Neural operators (LNO)[5], Fourier Neural operators (FNO)[6] and General Neural Operator Transformer for Operator learning (GNOT)[7]. In this paper, we focus on DeepONets as an operator learning technique and show a novel way on how to reduce the computational cost associated with training the model. DeepONet is based on the lesser known cousin of the'Universal Approximation

Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.