One of the best-performing models in cosmology is also one with the least physical rationale behind it. Can a theory of quantum gravity illuminate what happened just after the big bang? Cosmic inflation is a problem. During the first tiny fraction of a second of the universe, it is generally believed that the universe expanded by a factor of around 10. And then, as quickly as it began, this exponential growth just stopped.

The proof is given by [11]. Eq. (13)is clearlyO(3)-subequivariant, but theO(3)-subequivariant function is unnecessarily the form like Eq. (13). Then there must exit functionss( Z,h) and s ( Z,h), satisfying ˆf( Z,h) = [ Z, g]s( Z,h)+ Z s ( Z,h). Note thatf by Eq. (14) can also be considered as a function of both Z and g, and it is universal accordingtoProposition1. When f reducestoafunctionof Z byfixing g,thenbyTheorem1,itis 4 still universal with respect tothe subgroup that leaves g unchanged.

In this work, we propose Subequivariant Graph Neural Networks (SGNN) that consist of several features to tackle the above challenges.1.

In real-world decision-making tasks, learning an optimal policy without a trialand-error process is an appealing challenge. When expert demonstrations are available, imitation learning that mimics expert actions can learn a good policy efficiently.

Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization and should be incorporated into the model design. Existing simulators either consider insufficient symmetry, or enforce excessive equivariance in practice when symmetry is partially broken by gravity.

Science Space International Space Station Lost in space: How'digital twins' saved NASA's robots Navigation algorithms designed for Earth fail in orbit. Breakthroughs, discoveries, and DIY tips sent every weekday. A standard ballpoint pen will not write in space. Without gravity, the ink refuses to flow. This simple failure illustrates a profound headache in space exploration: tools designed for terrestrial use often become useless in a microgravity environment.

Are we living in a simulation? The idea that we might be living in a simulated reality has worried us for centuries. Thomas Anderson - otherwise known as Neo - is walking up a flight of stairs when he sees a black cat shake itself and walk past a doorway. Then the moment seems to replay before his eyes. Just a touch of déjà vu, he thinks.

Physicists finally know how much faster time moves on the Red Planet. Breakthroughs, discoveries, and DIY tips sent every weekday. Tracking the first astronauts' visit to Mars won't be as simple as watching a clock or marking days off of a calendar. Thanks to relativity, time actually moves faster on the Red Planet than it does here on Earth. For years, scientists have wondered about the exact temporal difference between planets, but physicists at the National Institute of Standards and Technology (NIST) finally have an answer.

Accurate state estimation for flexible robotic systems poses significant challenges, particular for platforms with dynamically deforming structures that invalidate rigid-body assumptions. This paper tackles this problem and allows to extend existing rigid-body pose estimation methods to non-rigid systems. Our approach hinges on two core assumptions: first, the elastic properties are captured by an injective deformation-force model, efficiently learned via a Multi-Layer Perceptron; second, we solve the platform's inherently smooth motion using continuous-time B-spline kinematic models. By continuously applying Newton's Second Law, our method establishes a physical link between visually-derived trajectory acceleration and predicted deformation-induced acceleration. We demonstrate that our approach not only enables robust and accurate pose estimation on non-rigid platforms, but that the properly modeled platform physics instigate inertial sensing properties. We demonstrate this feasibility on a simple spring-camera system, and show how it robustly resolves the typically ill-posed problem of metric scale and gravity recovery in monocular visual odometry.

Legged robots are promising candidates for exploring challenging areas on low-gravity bodies such as the Moon, Mars, or asteroids, thanks to their advanced mobility on unstructured terrain. However, as planetary robots' power and thermal budgets are highly restricted, these robots need energy-efficient control approaches that easily transfer to multiple gravity environments. In this work, we introduce a reinforcement learning-based control approach for legged robots with gravity-scaled power-optimized reward functions. We use our approach to develop and validate a locomotion controller and a base pose controller in gravity environments from lunar gravity (1.62 m/s2) to a hypothetical super-Earth (19.62 m/s2). Our approach successfully scales across these gravity levels for locomotion and base pose control with the gravity-scaled reward functions. The power-optimized locomotion controller reached a power consumption for locomotion of 23.4 W in Earth gravity on a 15.65 kg robot at 0.4 m/s, a 23 % improvement over the baseline policy. Additionally, we designed a constant-force spring offload system that allowed us to conduct real-world experiments on legged locomotion in lunar gravity. In lunar gravity, the power-optimized control policy reached 12.2 W, 36 % less than a baseline controller which is not optimized for power efficiency. Our method provides a scalable approach to developing power-efficient locomotion controllers for legged robots across multiple gravity levels.