Computational cardiovascular flow modeling plays a crucial role in understanding blood flow dynamics. While 3D models provide acute details, they are computationally expensive, especially with fluid-structure interaction (FSI) simulations. 1D models offer a computationally efficient alternative, by simplifying the 3D Navier-Stokes equations through axisymmetric flow assumption and cross-sectional averaging. However, traditional 1D models based on finite element methods (FEM) often lack accuracy compared to 3D averaged solutions. This study introduces a novel physics-constrained machine learning technique that enhances the accuracy of 1D blood flow models while maintaining computational efficiency. Our approach, utilizing a physics-constrained coupled neural differential equation (PCNDE) framework, demonstrates superior performance compared to conventional FEM-based 1D models across a wide range of inlet boundary condition waveforms and stenosis blockage ratios. A key innovation lies in the spatial formulation of the momentum conservation equation, departing from the traditional temporal approach and capitalizing on the inherent temporal periodicity of blood flow. This spatial neural differential equation formulation switches space and time and overcomes issues related to coupling stability and smoothness, while simplifying boundary condition implementation. The model accurately captures flow rate, area, and pressure variations for unseen waveforms and geometries. We evaluate the model's robustness to input noise and explore the loss landscapes associated with the inclusion of different physics terms. This advanced 1D modeling technique offers promising potential for rapid cardiovascular simulations, achieving computational efficiency and accuracy. By combining the strengths of physics-based and data-driven modeling, this approach enables fast and accurate cardiovascular simulations.

Since its modern inception in the pioneering computational work of Charney, Fjörtoft, and Von Neumann (see Charney et al. (1950)), numerical weather prediction (NWP) has proven to present formidable mathematical challenges. In particular, many dynamic models of weather phenomena exhibit multiscale and turbulent features which have been known since the seminal work of Lorenz (1963) to lead to a sensitive dependence on initial conditions. As a consequence, the uncertainties present in a set of initial observations grow exponentially in time under these models, bounding the predictive power of most numerical weather forecasts to medium-range time scales ( 14 days). This chaotic behavior is exacerbated by the computational reality that simulations of the relevant physics can only capture a finite range of scales, so that the physical influence of unresolved scales is either ignored or approximated by subgrid closure models. In recent years, there has been an explosion of interest surrounding data-driven approaches to weather modeling (see, e.g., Rasp et al. (2024) and Karlbauer et al. (2024) for a discussion and recent benchmarks). In contrast to traditional NWP, which relies on numerical simulations of physics-based weather models, these novel data-driven approaches learn effective weather models directly from empirical data.

Flight test analysis often requires predefined test points with arbitrarily tight tolerances, leading to extensive and resource-intensive experimental campaigns. To address this challenge, we propose a novel approach to flight test analysis using Gaussian processes (GPs) with physics-informed mean functions to estimate aerodynamic quantities from arbitrary flight test data, validated using real T-38 aircraft data collected in collaboration with the United States Air Force Test Pilot School. We demonstrate our method by estimating the pitching moment coefficient without requiring predefined or repeated flight test points, significantly reducing the need for extensive experimental campaigns. Our approach incorporates aerodynamic models as priors within the GP framework, enhancing predictive accuracy across diverse flight conditions and providing robust uncertainty quantification. Key contributions include the integration of physics-based priors in a probabilistic model, which allows for precise computation from arbitrary flight test maneuvers, and the demonstration of our method capturing relevant dynamic characteristics such as short-period mode behavior. The proposed framework offers a scalable and generalizable solution for efficient data-driven flight test analysis and is able to accurately predict the short period frequency and damping for the T-38 across several Mach and dynamic pressure profiles.

Limited accessibility to high field MRI scanners (such as 7T, 11T) has motivated the development of post-processing methods to improve low field images. Several existing post-processing methods have shown the feasibility to improve 3T images to produce 7T-like images [3,18]. It has been observed that improving lower field (LF, <=1.5T) images comes with additional challenges due to poor image quality such as the function mapping 1.5T and higher field (HF, 3T) images is more complex than the function relating 3T and 7T images [10]. Except for [10], no method has been addressed to improve <=1.5T MRI images. Further, most of the existing methods [3,18] including [10] require example images, and also often rely on pixel to pixel correspondences between LF and HF images which are usually inaccurate for <=1.5T images. The focus of this paper is to address the unsupervised framework for quality improvement of 1.5T images and avoid the expensive requirements of example images and associated image registration. The LF and HF images are assumed to be related by a linear transformation (LT). The unknown HF image and unknown LT are estimated in alternate minimization framework. Further, a physics based constraint is proposed that provides an additional non-linear function relating LF and HF images in order to achieve the desired high contrast in estimated HF image. The experimental results demonstrate that the proposed approach provides processed 1.5T images, i.e., estimated 3T-like images with improved image quality, and is comparably better than the existing methods addressing similar problems. The improvement in image quality is also shown to provide better tissue segmentation and volume quantification as compared to scanner acquired 1.5T images.

Physics-based dynamic models (PBDMs) are simplified representations of complex dynamical systems. PBDMs take specific processes within a complex system and assign a fragment of variables and an accompanying set of parameters to depict the processes. As this often leads to suboptimal parameterisation of the system, a key challenge requires refining the empirical parameters and variables to reduce uncertainties while maintaining the model's explainability and enhancing its predictive accuracy. We demonstrate that a hybrid mosquito population dynamics model, which integrates a PBDM with Physics-Informed Neural Networks (PINN), retains the explainability of the PBDM by incorporating the PINN-learned model parameters in place of its empirical counterparts. Specifically, we address the limitations of traditional PBDMs by modelling the parameters of larva and pupa development rates using a PINN that encodes complex, learned interactions of air temperature, precipitation and humidity. Our results demonstrate improved mosquito population simulations including the difficult-to-predict mosquito population peaks. This opens the possibility of hybridisation concept application on other complex systems based on PBDMs such as cancer growth to address the challenges posed by scarce and noisy data, and to numerical weather prediction and climate modelling to overcome the gap between physics-based and data-driven weather prediction models. Keywords: hybridisation, physics-based dynamic models, physics-informed neural networks (PINN), hybrid dynamic model, mosquito population modelling 1 Introduction Physics-based dynamic models (PBDMs) are widely used in research and technology, from predicting air temperature to modelling COVID-19 spread and cancer cell development.

In science and engineering, machine learning techniques are increasingly successful in physical systems modeling (predicting future states of physical systems). Effectively integrating PDE loss as a constraint of system transition can improve the model's prediction by overcoming generalization issues due to data scarcity, especially when data acquisition is costly. However, in many real-world scenarios, due to sensor limitations, the data we can obtain is often only partial observation, making the calculation of PDE loss seem to be infeasible, as the PDE loss heavily relies on high-resolution states. We carefully study this problem and propose a novel framework named Re-enable PDE Loss under Partial Observation (RPLPO). The key idea is that although enabling PDE loss to constrain system transition solely is infeasible, we can re-enable PDE loss by reconstructing the learnable high-resolution state and constraining system transition simultaneously. Specifically, RPLPO combines an encoding module for reconstructing learnable high-resolution states with a transition module for predicting future states. The two modules are jointly trained by data and PDE loss. We conduct experiments in various physical systems to demonstrate that RPLPO has significant improvement in generalization, even when observation is sparse, irregular, noisy, and PDE is inaccurate.

The growing threats of uncertainties, anomalies, and cyberattacks on power grids are driving a critical need to advance situational awareness which allows system operators to form a complete and accurate picture of the present and future state. Simulation and estimation are foundational tools in this process. However, existing tools lack the robustness and efficiency required to achieve the level of situational awareness needed for the ever-evolving threat landscape. Industry-standard (steady-state) simulators are not robust to blackouts, often leading to non-converging or non-actionable results. Estimation tools lack robustness to anomalous data, returning erroneous system states. Efficiency is the other major concern as nonlinearities and scalability issues make large systems slow to converge. This thesis addresses robustness and efficiency gaps through a dual-fold contribution. We first address the inherent limitations in the existing physics-based and data-driven worlds; and then transcend the boundaries of conventional algorithmic design in the direction of a new paradigm -- Physics-ML Synergy -- which integrates the strengths of the two worlds. Our approaches are built on circuit formulation which provides a unified framework that applies to both transmission and distribution. Sparse optimization acts as the key enabler to make these tools intrinsically robust and immune to random threats, pinpointing dominant sources of (random) blackouts and data errors. Further, we explore sparsity-exploiting optimizations to develop lightweight ML models whose prediction and detection capabilities are a complement to physics-based tools; and whose lightweight designs advance generalization and scalability. Finally, Physics-ML Synergy brings robustness and efficiency further against targeted cyberthreats, by interconnecting our physics-based tools with lightweight ML.

Estimates of seismic wave speeds in the Earth (seismic velocity models) are key input parameters to earthquake simulations for ground motion prediction. Owing to the non-uniqueness of the seismic inverse problem, typically many velocity models exist for any given region. The arbitrary choice of which velocity model to use in earthquake simulations impacts ground motion predictions. However, current hazard analysis methods do not account for this source of uncertainty. We present a proof-of-concept ground motion prediction workflow for incorporating uncertainties arising from inconsistencies between existing seismic velocity models. Our analysis is based on the probabilistic fusion of overlapping seismic velocity models using scalable Gaussian process (GP) regression. Specifically, we fit a GP to two synthetic 1-D velocity profiles simultaneously, and show that the predictive uncertainty accounts for the differences between the models. We subsequently draw velocity model samples from the predictive distribution and estimate peak ground displacement using acoustic wave propagation through the velocity models. The resulting distribution of possible ground motion amplitudes is much wider than would be predicted by simulating shaking using only the two input velocity models. This proof-of-concept illustrates the importance of probabilistic methods for physics-based seismic hazard analysis.

Large Language Models (LLMs) have shown state-of-the-art performance in a variety of tasks, including arithmetic and reasoning; however, to gauge the intellectual capabilities of LLMs, causal reasoning has become a reliable proxy for validating a general understanding of the mechanics and intricacies of the world similar to humans. Previous works in natural language processing (NLP) have either focused on open-ended causal reasoning via causal commonsense reasoning (CCR) or framed a symbolic representation-based question answering for theoretically backed-up analysis via a causal inference engine. The former adds an advantage of real-world grounding but lacks theoretically backed-up analysis/validation, whereas the latter is far from real-world grounding. In this work, we bridge this gap by proposing the COLD (Causal reasOning in cLosed Daily activities) framework, which is built upon human understanding of daily real-world activities to reason about the causal nature of events. We show that the proposed framework facilitates the creation of enormous causal queries (~ 9 million) and comes close to the mini-turing test, simulating causal reasoning to evaluate the understanding of a daily real-world task. We evaluate multiple LLMs on the created causal queries and find that causal reasoning is challenging even for activities trivial to humans. We further explore (the causal reasoning abilities of LLMs) using the backdoor criterion to determine the causal strength between events.

In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial intelligence algorithms to solve partial differential equations (AI for PDEs: Artificial intelligence for partial differential equations) has become a focal point in computational mechanics. The core of AI for PDEs is the fusion of data and partial differential equations (PDEs), which can solve almost any PDEs. Therefore, this article provides a comprehensive review of the research on AI for PDEs, summarizing the existing algorithms and theories. The article discusses the applications of AI for PDEs in computational mechanics, including solid mechanics, fluid mechanics, and biomechanics. The existing AI for PDEs algorithms include those based on Physics-Informed Neural Networks (PINNs), Deep Energy Methods (DEM), Operator Learning, and Physics-Informed Neural Operator (PINO). AI for PDEs represents a new method of scientific simulation that provides approximate solutions to specific problems using large amounts of data, then fine-tuning according to specific physical laws, avoiding the need to compute from scratch like traditional algorithms. Thus, AI for PDEs is the prototype for future foundation models in computational mechanics, capable of significantly accelerating traditional numerical algorithms.