While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison. We have conducted extensive experiments with these methods, offering insights into their strengths and weaknesses. In addition to providing a standardized means of assessing performance, PINNacle also offers an in-depth analysis to guide future research, particularly in areas such as domain decomposition methods and loss reweighting for handling multi-scale problems and complex geometry. To the best of our knowledge, it is the largest benchmark with a diverse and comprehensive evaluation that will undoubtedly foster further research in PINNs.

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle, a benchmarking tool designed to fill this gap. PINNacle provides a diverse dataset, comprising over 20 distinct PDEs from various domains, including heat conduction, fluid dynamics, biology, and electromagnetics. These PDEs encapsulate key challenges inherent to real-world problems, such as complex geometry, multi-scale phenomena, nonlinearity, and high dimensionality. PINNacle also offers a user-friendly toolbox, incorporating about 10 state-of-the-art PINN methods for systematic evaluation and comparison.

Physics-Informed Neural Networks (PINNs), which incorporate PDEs as soft constraints, train with a composite loss function that contains multiple training point types: different types of collocation points chosen during training to enforce each PDE and initial/boundary conditions, and experimental points which are usually costly to obtain via experiments or simulations. Training PINNs using this loss function is challenging as it typically requires selecting large numbers of points of different types, each with different training dynamics. PINNACLE uses information on the interaction among training point types, which had not been considered before, based on an analysis of PINN training dynamics via the Neural Tangent Kernel (NTK). We theoretically show that the criterion used by PINNACLE is related to the PINN generalization error, and empirically demonstrate that PINNACLE is able to outperform existing point selection methods for forward, inverse, and transfer learning problems. Deep learning (DL) successes in domains with massive datasets have led to questions on whether it can also be efficiently applied to the scientific domains. In these settings, while training data may be more limited, domain knowledge could compensate by serving as inductive biases for DL training. Such knowledge can take the form of governing Partial Differential Equations (PDEs), which can describe phenomena such as conservation laws or dynamic system evolution in areas such as fluid dynamics (Cai et al., 2021; Chen et al., 2021; Jagtap et al., 2022), wave propagation and optics (bin Waheed et al., 2021; Lin & Chen, 2022), or epidemiology (Rodríguez et al., 2023). Physics-Informed Neural Networks (PINNs) are neural networks that incorporate PDEs and their initial/boundary conditions (IC/BCs) as soft constraints during training (Raissi et al., 2019), and have been successfully applied to various problems. These include forward problems (i.e., predicting PDE solutions given specified PDEs and ICs/BCs) and inverse problems (i.e., learning unknown PDE parameters given experimental data). However, the training of PINNs is challenging. Past works have tried to separately address these individually by considering an adaptive selection of CL points (Nabian et al., 2021; Gao & Wang, 2023; Wu et al., 2023; Peng et al., 2022; Zeng et al., 2022; Tang et al., 2023), or E Some works have also proposed heuristics that adjust loss term weights of the various point types to try improve training dynamics, but do not consider point selection (Wang et al., 2022c). However, no work thus far has looked into optimizing all training point types jointly to significantly boost PINN performance. Given that the solution spaces of the PDE, IC/BC and underlying output function are tightly coupled, it is inefficient and sub-optimal to select each type of training points separately and ignore cross information across point types.

Most smart-home gadget manufacturers would have you believe that tapping an app is the pinnacle of convenience. What if it was a speaker that could also answer questions? It's all fun and games until the smart system breaks down and turns it into something worse than an old-fashioned dumb gadget. A camera is just a camera, unless it's a compromised security camera that threatens to show everyone in the world your home address. A bed is (usually) just a bed, unless, in my case, you're sleeping on a smart bed stuck halfway between Flat and Zero Gravity modes.

In the majority of fiction that concerns artificial intelligence (AI), it replaces us in almost every industry. Often, only the artistic fields are left untouched. Usually, a robot or AI showing capabilities to create a work is seen as a completion, at the pinnacle of intelligence, considered almost human. Yet, AI and the arts are already flirting in reality, whether in music creation or visual arts, it is becoming more and more present. However, on August 26, 2022, there was a rude shock when, at a visual arts competition in Colorado, the winning image was entirely designed by an AI.

Smart cities are no longer a utopian dream of the future. Thanks to a slew of innovative and game-changing technologies, they are already active and growing quickly. Smart cities could be described as the junction between three main areas, namely digital transformation, environmental sustainability and economic performance. They can be described as a framework made up of connected technologies designed to address the challenges of rapid urbanisation and promote more sustainable, smarter practices. And the more urbanisation soars, standards of living sustainability become more than pipe dreams, but rather calls for action.

Fan Hui, the European Go champion, needed some fresh air. "I don't understand myself anymore." Hui was the first professional Go player to face AlphaGo, Google's artificial intelligence system and the title of a new documentary by Greg Kohs that debuted last week at the Tribeca Film Festival in New York. When Hui was invited to visit Google's London office housing the DeepMind research group that developed AlphaGo, he was feeling confident. After all, as Hui puts it, "it is just a program."

Fan Hui, the European Go champion, needed some fresh air. "I don't understand myself anymore." Hui was the first professional Go player to face AlphaGo, Google's artificial intelligence system and the title of a new documentary by Greg Kohs that debuted last week at the Tribeca Film Festival in New York. When Hui was invited to visit Google's London office housing the DeepMind research group that developed AlphaGo, he was feeling confident. After all, as Hui puts it, "it is just a program."

While pain can be an unpleasant experience, it is a fundamental mechanism in organisms to help them identify threats. But should robots be programmed to experience pain? A new documentary from Cambridge University tackles this divisive issue, looking at the philosophical, ethical and social questions involved with artificially programming pain responses. Science fiction author Isaac Asimov first came up with the three'laws' of robotics in a story called'Runaround', published in 1942. The first of these laws says a robot may not injure a human being or, through inaction, allow a human being to come to harm.

Spot the Robot Dog gets kicked. Why was I programmed to feel pain?" The question is played for laughs, but like so many memorable scenes from this most beloved of shows, it also taps into some of the deeper, overarching themes that define our modern civilization. Pain is a fundamental fact of life for many organisms on our planet; a crucial mechanism for identifying what kinds of actions pose serious threats to our physical and mental health. As robots become more sophisticated and interactive, should they also be programmed to experience pain to prevent injuries to themselves or others, and if so, to what extent? "Pain in the Machine," a 12-minute documentary released by the University of Cambridge on Monday, tackles this multifaceted and controversial issue. The film offers insights from artificial intelligence thought leaders, practicing physicians, and other interdisciplinary experts, and contrasts them with iconic popular culture moments that point to the larger philosophical questions inherent to artificially programming pain responses--including a nod to burning robot bit in The Simpsons. Like so many AI research fields, evaluating the utility and benefits of pain in robots inevitably flips the mirror back on our understanding of how those experiences function and protect us in our own lives. "Pain has fascinated philosophers for centuries," Ben Seymour, a Cambridge-based expert on the computational and systems neuroscience of pain, comments in the documentary. "Indeed, some people consider pain to be the pinnacle of consciousness.