The Ornstein-Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.

Performing tasks in a physical environment is a crucial yet challenging problem for AI systems operating in the real world. Physics simulation-based tasks are often employed to facilitate research that addresses this challenge. In this paper, first, we present a systematic approach for defining a physical scenario using a causal sequence of physical interactions between objects. Then, we propose a methodology for generating tasks in a physics-simulating environment using these defined scenarios as inputs. Our approach enables a better understanding of the granular mechanics required for solving physics-based tasks, thereby facilitating accurate evaluation of AI systems' physical reasoning capabilities. We demonstrate our proposed task generation methodology using the physics-based puzzle game Angry Birds and evaluate the generated tasks using a range of metrics, including physical stability, solvability using intended physical interactions, and accidental solvability using unintended solutions. We believe that the tasks generated using our proposed methodology can facilitate a nuanced evaluation of physical reasoning agents, thus paving the way for the development of agents for more sophisticated real-world applications.

Long-span bridges are subjected to a multitude of dynamic excitations during their lifespan. To account for their effects on the structural system, several load models are used during design to simulate the conditions the structure is likely to experience. These models are based on different simplifying assumptions and are generally guided by parameters that are stochastically identified from measurement data, making their outputs inherently uncertain. This paper presents a probabilistic physics-informed machine-learning framework based on Gaussian process regression for reconstructing dynamic forces based on measured deflections, velocities, or accelerations. The model can work with incomplete and contaminated data and offers a natural regularization approach to account for noise in the measurement system. An application of the developed framework is given by an aerodynamic analysis of the Great Belt East Bridge. The aerodynamic response is calculated numerically based on the quasi-steady model, and the underlying forces are reconstructed using sparse and noisy measurements. Results indicate a good agreement between the applied and the predicted dynamic load and can be extended to calculate global responses and the resulting internal forces. Uses of the developed framework include validation of design models and assumptions, as well as prognosis of responses to assist in damage detection and structural health monitoring.

In private federated learning (FL), a server aggregates differentially private updates from a large number of clients in order to train a machine learning model. The main challenge in this setting is balancing privacy with both classification accuracy of the learnt model as well as the number of bits communicated between the clients and server. Prior work has achieved a good trade-off by designing a privacy-aware compression mechanism, called the minimum variance unbiased (MVU) mechanism, that numerically solves an optimization problem to determine the parameters of the mechanism. This paper builds upon it by introducing a new interpolation procedure in the numerical design process that allows for a far more efficient privacy analysis. The result is the new Interpolated MVU mechanism that is more scalable, has a better privacy-utility trade-off, and provides SOTA results on communication-efficient private FL on a variety of datasets.

State-of-the-art approaches to footstep planning assume reduced-order dynamics when solving the combinatorial problem of selecting contact surfaces in real time. However, in exchange for computational efficiency, these approaches ignore joint torque limits and limb dynamics. In this work, we address these limitations by presenting a topology-based approach that enables model predictive control (MPC) to simultaneously plan full-body motions, torque commands, footstep placements, and contact surfaces in real time. To determine if a robot's foot is inside a contact surface, we borrow the winding number concept from topology. We then use this winding number and potential field to create a contact-surface penalty function. By using this penalty function, MPC can select a contact surface from all candidate surfaces in the vicinity and determine footstep placements within it. We demonstrate the benefits of our approach by showing the impact of considering full-body dynamics, which includes joint torque limits and limb dynamics, on the selection of footstep placements and contact surfaces. Furthermore, we validate the feasibility of deploying our topology-based approach in an MPC scheme and explore its potential capabilities through a series of experimental and simulation trials.

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first hybrid approach incorporating data and PDE constraints at different resolutions to learn the operator. Specifically, in PINO, we combine coarse-resolution training data with PDE constraints imposed at a higher resolution. The resulting PINO model can accurately approximate the ground-truth solution operator for many popular PDE families and shows no degradation in accuracy even under zero-shot super-resolution, i.e., being able to predict beyond the resolution of training data. PINO uses the Fourier neural operator (FNO) framework that is guaranteed to be a universal approximator for any continuous operator and discretization-convergent in the limit of mesh refinement. By adding PDE constraints to FNO at a higher resolution, we obtain a high-fidelity reconstruction of the ground-truth operator. Moreover, PINO succeeds in settings where no training data is available and only PDE constraints are imposed, while previous approaches, such as the Physics-Informed Neural Network (PINN), fail due to optimization challenges, e.g., in multi-scale dynamic systems such as Kolmogorov flows.

As medical ultrasound is becoming a prevailing examination approach nowadays, robotic ultrasound systems can facilitate the scanning process and prevent professional sonographers from repetitive and tedious work. Despite the recent progress, it is still a challenge to enable robots to autonomously accomplish the ultrasound examination, which is largely due to the lack of a proper task representation method, and also an adaptation approach to generalize learned skills across different patients. To solve these problems, we propose the latent task representation and the robotic skills adaptation for autonomous ultrasound in this paper. During the offline stage, the multimodal ultrasound skills are merged and encapsulated into a low-dimensional probability model through a fully self-supervised framework, which takes clinically demonstrated ultrasound images, probe orientations, and contact forces into account. During the online stage, the probability model will select and evaluate the optimal prediction. For unstable singularities, the adaptive optimizer fine-tunes them to near and stable predictions in high-confidence regions. Experimental results show that the proposed approach can generate complex ultrasound strategies for diverse populations and achieve significantly better quantitative results than our previous method.

However, despite its potential, metal AM has not yet reached its expected level of usage in industries, in part due to a lack of accurate prediction of the properties of printed components. For example, in laser powder bed fusion (LPBF), the layer of metal powder is scanned by a laser heat source which converts the metal powder to liquid, which eventually solidifies and converts to the final product. Accurate thermal history prediction is crucial for LPBF, as all other phenomena, including thermal residual stress and microstructure, depend on it. The melt pool dynamics play a very important role in the development of the thermal map for LPBF. Many factors influence the melt pool dynamics in LPBF such as the unique thermal cycle of rapid heating and solidification, steep temperature gradient and high cooling rate, evaporation, surface tension, natural convection, Marangoni convection, vapor recoil pressure, and Argon flow over the melt pool. Several researchers have developed computational models to better understand melt pool dynamics, incorporating these complex phenomena [1-5]. Physics-based simulation such as computational fluid dynamics (CFD) is the key method to model melt pool dynamics (Figure 1). Li et al. [6] utilized a 2D model to examine the melting and

Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to perform efficiently in cases of data scarcity. To deal with such issues, combination of physics-based approaches and machine learning algorithms have been developed. Although such methods are effective, they also require the analyser's understanding of the underlying physics of the problem. The current work is aimed at motivating the use of models which learn such relationships from a population of phenomena, whose underlying physics are similar. The development of such models is motivated by the way that physics-based models, and more specifically finite element models, work. Such models are considered transferrable, explainable and trustworthy, attributes which are not trivially imposed or achieved for machine-learning models. For this reason, machine-learning approaches are less trusted by industry and often considered more difficult to form validated models. To achieve such data-driven models, a population-based scheme is followed here and two different machine-learning algorithms from the meta-learning domain are used. The two algorithms are the model-agnostic meta-learning (MAML) algorithm and the conditional neural processes (CNP) model. The algorithms seem to perform as intended and outperform a traditional machine-learning algorithm at approximating the quantities of interest. Moreover, they exhibit behaviour similar to traditional machine learning algorithms (e.g. neural networks or Gaussian processes), concerning their performance as a function of the available structures in the training population.

Although deep learning has achieved remarkable success in various scientific machine learning applications, its black-box nature poses concerns regarding interpretability and generalization capabilities beyond the training data. Interpretability is crucial and often desired in modeling physical systems. Moreover, acquiring extensive datasets that encompass the entire range of input features is challenging in many physics-based learning tasks, leading to increased errors when encountering out-of-distribution (OOD) data. In this work, motivated by the field of functional data analysis (FDA), we propose generalized functional linear models as an interpretable surrogate for a trained deep learning model. We demonstrate that our model could be trained either based on a trained neural network (post-hoc interpretation) or directly from training data (interpretable operator learning). A library of generalized functional linear models with different kernel functions is considered and sparse regression is used to discover an interpretable surrogate model that could be analytically presented. We present test cases in solid mechanics, fluid mechanics, and transport. Our results demonstrate that our model can achieve comparable accuracy to deep learning and can improve OOD generalization while providing more transparency and interpretability. Our study underscores the significance of interpretability in scientific machine learning and showcases the potential of functional linear models as a tool for interpreting and generalizing deep learning.