Neural PDEs have emerged as inexpensive surrogate models for numerical PDE solvers. While they offer efficient approximations, they often lack robust uncertainty quantification (UQ), limiting their practical utility. Existing UQ methods for these models typically have high computational demands and lack guarantees. We introduce a novel framework for calibrated physics-informed uncertainty quantification to address these limitations. Our approach leverages physics residual errors as a nonconformity score within a conformal prediction (CP) framework. This enables data-free, model-agnostic, and statistically guaranteed uncertainty estimates. Our framework utilises convolutional layers as finite difference stencils for gradient estimation, our framework provides inexpensive coverage bounds for the violation of conservation laws within model predictions. In our experiments, we utilise CP to obtain marginal coverage for each cell and joint coverage over the entire prediction domain of various PDEs.

This article focuses on predicting how an object can be transformed to a semantically meaningful pose relative to another object, given only one or few examples. Current pose correspondence methods rely on vast 3D object datasets and do not actively consider semantic information, which limits the objects to which they can be applied. We present a novel method for learning cross-object pose correspondence. The proposed method detects interacting object parts, performs one-shot part correspondence, and uses geometric and visual-semantic features. Given one example of two objects posed relative to each other, the model can learn how to transfer the demonstrated relations to unseen object instances.

In recent years, machine learning has established itself as a powerful tool for high-resolution weather forecasting. While most current machine learning models focus on deterministic forecasts, accurately capturing the uncertainty in the chaotic weather system calls for probabilistic modeling. We propose a probabilistic weather forecasting model called Graph-EFM, combining a flexible latent-variable formulation with the successful graph-based forecasting framework. The use of a hierarchical graph construction allows for efficient sampling of spatially coherent forecasts. Requiring only a single forward pass per time step, Graph-EFM allows for fast generation of arbitrarily large ensembles. We experiment with the model on both global and limited area forecasting. Ensemble forecasts from Graph-EFM achieve equivalent or lower errors than comparable deterministic models, with the added benefit of accurately capturing forecast uncertainty.

Global convolutions have shown increasing promise as powerful general-purpose sequence models. However, training long convolutions is challenging, and kernel parameterizations must be able to learn long-range dependencies without overfitting. This work introduces reparameterized multi-resolution convolutions (MRConv), a novel approach to parameterizing global convolutional kernels for long-sequence modelling. By leveraging multi-resolution convolutions, incorporating structural reparameterization and introducing learnable kernel decay, MRConv learns expressive long-range kernels that perform well across various data modalities. Our experiments demonstrate state-of-the-art performance on the Long Range Arena, Sequential CIFAR, and Speech Commands tasks among convolution models and linear-time transformers. Moreover, we report improved performance on ImageNet classification by replacing 2D convolutions with 1D MRConv layers.

Unlike traditional rigid robots, soft robots offer more flexibility, compliance, and adaptability. They are also typically cheaper to manufacture and are lighter than their rigid counterparts. However, due to modeling difficulties, real-world applications for soft robots are still limited. This is especially true for applications that would require dynamic or fast motion. In addition, their operating principles and compliance make integrating effective proprioceptive sensors difficult. As such, state estimation and predictions of how the state evolves in time are challenging modeling tasks. Large-scale ($≈$ two meters in length), particularly fluid-driven, soft robots have greater modeling complexity due to increased inertia and related effects of gravity. Few approaches to soft robot control (learned or model-based) have enabled dynamic motion such as throwing or hammering since most methods require limiting assumptions about the kinematics, dynamics, or actuation models to make the control problem tractable or performant. To address this issue, we propose using Bayesian optimization to learn policies for dynamic tasks on a large-scale soft robot. This approach optimizes the task objective function directly from commanded pressures, without requiring approximate kinematics or dynamics as an intermediate step. We also present simulated and real-world experiments to illustrate the efficacy of the proposed approach.