Air pollution remains one of the most critical environmental challenges globally, posing severe threats to public health, ecological sustainability, and climate governance. While existing physics-based and data-driven models have made progress in air quality forecasting, they often struggle to jointly capture the complex spatiotemporal dynamics and ensure spatial continuity of pollutant distributions. In this study, we introduce CTENet, a novel chemical transport deep learning model that embeds the Advection-Diffusion-Reaction equation into a Physics-Informed Neural Network (PINN) framework using an Eulerian representation to model the spatiotemporal evolution of pollutants. Extensive experiments on two realworld datasets demonstrate that CTENet consistently outperforms state-of-the-art (SOTA) baselines, achieving a remarkable RMSE improvement of 45.8% on the USA dataset and 21.0% on the China dataset.

Tropical Cyclone (TC) estimation aims to accurately estimate various TC attributes in real time.

Dynamic manipulation, such as robot tossing or throwing objects, has recently gained attention as a novel paradigm to speed up logistic operations. However, the focus has predominantly been on the object's landing location, irrespective of its final orientation. In this work, we present a method enabling a robot to accurately "throw-flip" objects to a desired landing pose (position and orientation). Conventionally, objects thrown by revolute robots suffer from parasitic rotation, resulting in highly restricted and uncontrollable landing poses. Our approach is based on two key design choices: first, leveraging the impulse-momentum principle, we design a family of throwing motions that effectively decouple the parasitic rotation, significantly expanding the feasible set of landing poses. Second, we combine a physics-based model of free flight with regression-based learning methods to account for unmodeled effects. Real robot experiments demonstrate that our framework can learn to throw-flip objects to a pose target within ($\pm$5 cm, $\pm$45 degrees) threshold in dozens of trials. Thanks to data assimilation, incorporating projectile dynamics reduces sample complexity by an average of 40% when throw-flipping to unseen poses compared to end-to-end learning methods. Additionally, we show that past knowledge on in-hand object spinning can be effectively reused, accelerating learning by 70% when throwing a new object with a Center of Mass (CoM) shift. A video summarizing the proposed method and the hardware experiments is available at https://youtu.be/txYc9b1oflU.

The relative balance between physics and data within any physics-informed machine learner is an important modelling consideration to ensure that the benefits of both physics and data-based approaches are maximised. An over reliance on physical knowledge can be detrimental, particularly when the physics-based component of a model may not accurately represent the true underlying system. An underutilisation of physical knowledge potentially wastes a valuable resource, along with benefits in model interpretability and reduced demand for expensive data collection. Achieving an optimal physics-data balance is a challenging aspect of model design, particularly if the level varies through time; for example, one might have a physical approximation, only valid within particular regimes, or a physical phenomenon may be known to only occur when given conditions are met (e.g. at high temperatures). This paper develops novel, physically-informed, change-point kernels for Gaussian processes, capable of dynamically varying the reliance upon available physical knowledge. A high level of control is granted to a user, allowing for the definition of conditions in which they believe a phenomena should occur and the rate at which the knowledge should be phased in and out of a model. In circumstances where users may be less certain, the switching reliance upon physical knowledge may be automatically learned and recovered from the model in an interpretable and intuitive manner. Variation of the modelled noise based on the physical phenomena occurring is also implemented to provide a more representative capture of uncertainty alongside predictions. The capabilities of the new kernel structures are explored through the use of two engineering case studies: the directional wind loading of a cable-stayed bridge and the prediction of aircraft wing strain during in-flight manoeuvring.

As children grow older, they develop an intuitive understanding of the physical processes around them. Their physical understanding develops in stages, moving along developmental trajectories which have been mapped out extensively in previous empirical research. Here, we investigate how the learning trajectories of deep generative neural networks compare to children's developmental trajectories using physical understanding as a testbed. We outline an approach that allows us to examine two distinct hypotheses of human development - stochastic optimization and complexity increase. We find that while our models are able to accurately predict a number of physical processes, their learning trajectories under both hypotheses do not follow the developmental trajectories of children.

In this paper, we propose the Phy-DRL: a physics-model-regulated deep reinforcement learning framework for safety-critical autonomous systems. The Phy-DRL is unique in three innovations: i) proactive unknown-unknowns training, ii) conjunctive residual control (i.e., integration of data-driven control and physics-model-based control) and safety- \& stability-sensitive reward, and iii) physics-model-based neural network editing, including link editing and activation editing. Thanks to the concurrent designs, the Phy-DRL is able to 1) tolerate unknown-unknowns disturbances, 2) guarantee mathematically provable safety and stability, and 3) strictly comply with physical knowledge pertaining to Bellman equation and reward. The effectiveness of the Phy-DRL is finally validated by an inverted pendulum and a quadruped robot. The experimental results demonstrate that compared with purely data-driven DRL, Phy-DRL features remarkably fewer learning parameters, accelerated training and enlarged reward, while offering enhanced model robustness and safety assurance.

Traditionally, numerical models have been deployed in oceanography studies to simulate ocean dynamics by representing physical equations. However, many factors pertaining to ocean dynamics seem to be ill-defined. We argue that transferring physical knowledge from observed data could further improve the accuracy of numerical models when predicting Sea Surface Temperature (SST). Recently, the advances in earth observation technologies have yielded a monumental growth of data. Consequently, it is imperative to explore ways in which to improve and supplement numerical models utilizing the ever-increasing amounts of historical observational data. To this end, we introduce a method for SST prediction that transfers physical knowledge from historical observations to numerical models. Specifically, we use a combination of an encoder and a generative adversarial network (GAN) to capture physical knowledge from the observed data. The numerical model data is then fed into the pre-trained model to generate physics-enhanced data, which can then be used for SST prediction. Experimental results demonstrate that the proposed method considerably enhances SST prediction performance when compared to several state-of-the-art baselines.

We implement a Physics-Informed Neural Network (PINN) for solving the two-dimensional Burgers equations. This type of model can be trained with no previous knowledge of the solution; instead, it relies on evaluating the governing equations of the system in points of the physical domain. It is also possible to use points with a known solution during training. In this paper, we compare PINNs trained with different amounts of governing equation evaluation points and known solution points. Comparing models that were trained purely with known solution points to those that have also used the governing equations, we observe an improvement in the overall observance of the underlying physics in the latter. We also investigate how changing the number of each type of point affects the resulting models differently. Finally, we argue that the addition of the governing equations during training may provide a way to improve the overall performance of the model without relying on additional data, which is especially important for situations where the number of known solution points is limited.

Purely data-driven deep neural networks (DNNs) applied to physical engineering systems can infer relations that violate physics laws, thus leading to unexpected consequences. To address this challenge, we propose a physics-model-based DNN framework, called Phy-Taylor, that accelerates learning compliant representations with physical knowledge. The Phy-Taylor framework makes two key contributions; it introduces a new architectural Physics-compatible neural network (PhN), and features a novel compliance mechanism, we call {\em Physics-guided Neural Network Editing\}. The PhN aims to directly capture nonlinearities inspired by physical quantities, such as kinetic energy, potential energy, electrical power, and aerodynamic drag force. To do so, the PhN augments neural network layers with two key components: (i) monomials of Taylor series expansion of nonlinear functions capturing physical knowledge, and (ii) a suppressor for mitigating the influence of noise. The neural-network editing mechanism further modifies network links and activation functions consistently with physical knowledge. As an extension, we also propose a self-correcting Phy-Taylor framework that introduces two additional capabilities: (i) physics-model-based safety relationship learning, and (ii) automatic output correction when violations of safety occur. Through experiments, we show that (by expressing hard-to-learn nonlinearities directly and by constraining dependencies) Phy-Taylor features considerably fewer parameters, and a remarkably accelerated training process, while offering enhanced model robustness and accuracy.

Abstract--Imposing physical constraints on neural networks as a method of knowledge embedding has achieved great progress in solving physical problems described by governing equations. However, for many engineering problems, governing equations often have complex forms, including complex partial derivatives or stochastic physical fields, which results in significant inconveniences from the perspective of implementation. In this paper, a scientific machine learning framework, called AutoKE, is proposed, and a reservoir flow problem is taken as an instance to demonstrate that this framework can effectively automate the process of embedding physical knowledge. In AutoKE, an emulator comprised of deep neural networks (DNNs) is built for predicting the physical variables of interest. An arbitrarily complex equation can be parsed and automatically converted into a computational graph through the equation parser module, and the fitness of the emulator to the governing equation is evaluated via automatic differentiation. Furthermore, the fixed weights in the loss function are substituted with adaptive weights by incorporating the Lagrangian dual method. Neural architecture search (NAS) is also introduced into the AutoKE to select an optimal network architecture of the emulator according to the specific problem. Finally, we apply transfer learning to enhance the scalability of the emulator. In experiments, the framework is verified by a series of physical problems in which it can automatically embed physical knowledge into an emulator without heavy hand-coding. The results demonstrate that the emulator can not only make accurate predictions, but also be applied to similar problems with high efficiency via transfer learning. Impact Statement -- Embedding physical knowledge into machine learning has been widely applied in solving scientific computing problems. However, it is tedious and time-consuming to establish the emulator and embed physical knowledge into it.