Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the Lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects.

We present a causal intervention module (CIM) to improve object detection methods. State-of-the-art object detectors learn the association between image pixels and bounding boxes with labels, which implicitly use contextual information in the backbone. Intuitively, context is such a rich source of information that an improvement due to contextual information is relatively modest. Inspired by this, we use the context explicitly in a novel framework of causal intervention for object detection. Specifically, we use a structural causal model to reveal how context confounders affect the object detection model, and adopt causal intervention to deal with the effect. The proposed CIM is applied to a two-stage object detection baseline, and extensive experiments show its effectiveness.