Machine Learning with Physics Knowledge for Prediction: A Survey

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest due to their potential impact on advancing scientific research and industrial practices by improving predictive models with small- or large-scale datasets and expressive predictive models with useful inductive biases. The survey has two parts. The first considers incorporating physics knowledge on an architectural level through objective functions, structured predictive models, and data augmentation. The second considers data as physics knowledge, which motivates looking at multi-task, meta, and contextual learning as an alternative approach to incorporating physics knowledge in a data-driven fashion. Finally, we also provide an industrial perspective on the application of these methods and a survey of the open-source ecosystem for physics-informed machine learning.

Dude: Dual Distribution-Aware Context Prompt Learning For Large Vision-Language Model

Prompt learning methods are gaining increasing attention due to their ability to customize large vision-language models to new domains using pre-trained contextual knowledge and minimal training data. However, existing works typically rely on optimizing unified prompt inputs, often struggling with fine-grained classification tasks due to insufficient discriminative attributes. To tackle this, we consider a new framework based on a dual context of both domain-shared and class-specific contexts, where the latter is generated by Large Language Models (LLMs) such as GPTs. Such dual prompt methods enhance the model's feature representation by joining implicit and explicit factors encoded in LLM knowledge. Moreover, we formulate the Unbalanced Optimal Transport (UOT) theory to quantify the relationships between constructed prompts and visual tokens. Through partial matching, UOT can properly align discrete sets of visual tokens and prompt embeddings under different mass distributions, which is particularly valuable for handling irrelevant or noisy elements, ensuring that the preservation of mass does not restrict transport solutions. Furthermore, UOT's characteristics integrate seamlessly with image augmentation, expanding the training sample pool while maintaining a reasonable distance between perturbed images and prompt inputs. Extensive experiments across few-shot classification and adapter settings substantiate the superiority of our model over current state-of-the-art baselines.

Structure-Aware E(3)-Invariant Molecular Conformer Aggregation Networks

A molecule's 2D representation consists of its atoms, their attributes, and the molecule's covalent bonds. A 3D (geometric) representation of a molecule is called a conformer and consists of its atom types and Cartesian coordinates. Every conformer has a potential energy, and the lower this energy, the more likely it occurs in nature. Most existing machine learning methods for molecular property prediction consider either 2D molecular graphs or 3D conformer structure representations in isolation. Inspired by recent work on using ensembles of conformers in conjunction with 2D graph representations, we propose E(3)-invariant molecular conformer aggregation networks. The method integrates a molecule's 2D representation with that of multiple of its conformers. Contrary to prior work, we propose a novel 2D--3D aggregation mechanism based on a differentiable solver for the \emph{Fused Gromov-Wasserstein Barycenter} problem and the use of an efficient online conformer generation method based on distance geometry. We show that the proposed aggregation mechanism is E(3) invariant and provides an efficient GPU implementation. Moreover, we demonstrate that the aggregation mechanism helps to outperform state-of-the-art property prediction methods on established datasets significantly.

Accelerating Motion Planning via Optimal Transport

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to issues like high planning times that hinder real-time, efficient decision-making. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods might suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of easy access to objectives-gradients. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) - a gradient-free method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process dynamics prior via planning-as-inference perspective. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule -- the Sinkhorn Step, which uses the regular polytope family for its search directions; each regular polytope, centered on trajectory waypoints, serves as a local neighborhood, effectively acting as a trust region, where the Sinkhorn Step "transports" local waypoints toward low-cost regions. We theoretically show that Sinkhorn Step guides the optimizing parameters toward local minima regions on non-convex objective functions. We then show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared with popular motion planners and paving the way for new applications of optimal transport in motion planning.

Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models

Learning priors on trajectory distributions can help accelerate robot motion planning optimization. Given previously successful plans, learning trajectory generative models as priors for a new planning problem is highly desirable. Prior works propose several ways on utilizing this prior to bootstrapping the motion planning problem. Either sampling the prior for initializations or using the prior distribution in a maximum-a-posterior formulation for trajectory optimization. In this work, we propose learning diffusion models as priors. We then can sample directly from the posterior trajectory distribution conditioned on task goals, by leveraging the inverse denoising process of diffusion models. Furthermore, diffusion has been recently shown to effectively encode data multimodality in high-dimensional settings, which is particularly well-suited for large trajectory dataset. To demonstrate our method efficacy, we compare our proposed method - Motion Planning Diffusion - against several baselines in simulated planar robot and 7-dof robot arm manipulator environments. To assess the generalization capabilities of our method, we test it in environments with previously unseen obstacles. Our experiments show that diffusion models are strong priors to encode high-dimensional trajectory distributions of robot motions.

Hierarchical Policy Blending As Optimal Transport

We present hierarchical policy blending as optimal transport (HiPBOT). This hierarchical framework adapts the weights of low-level reactive expert policies, adding a look-ahead planning layer on the parameter space of a product of expert policies and agents. Our high-level planner realizes a policy blending via unbalanced optimal transport, consolidating the scaling of underlying Riemannian motion policies, effectively adjusting their Riemannian matrix, and deciding over the priorities between experts and agents, guaranteeing safety and task success. Our experimental results in a range of application scenarios from low-dimensional navigation to high-dimensional whole-body control showcase the efficacy and efficiency of HiPBOT, which outperforms state-of-the-art baselines that either perform probabilistic inference or define a tree structure of experts, paving the way for new applications of optimal transport to robot control. More material at https://sites.google.com/view/hipobot

Learning Implicit Priors for Motion Optimization

In this paper, we focus on the problem of integrating Energy-based Models (EBM) as guiding priors for motion optimization. EBMs are a set of neural networks that can represent expressive probability density distributions in terms of a Gibbs distribution parameterized by a suitable energy function. Due to their implicit nature, they can easily be integrated as optimization factors or as initial sampling distributions in the motion optimization problem, making them good candidates to integrate data-driven priors in the motion optimization problem. In this work, we present a set of required modeling and algorithmic choices to adapt EBMs into motion optimization. We investigate the benefit of including additional regularizers in the learning of the EBMs to use them with gradient-based optimizers and we present a set of EBM architectures to learn generalizable distributions for manipulation tasks. We present multiple cases in which the EBM could be integrated for motion optimization and evaluate the performance of learned EBMs as guiding priors for both simulated and real robot experiments.

Learning Forceful Manipulation Skills from Multi-modal Human Demonstrations

Learning from Demonstration (LfD) provides an intuitive and fast approach to program robotic manipulators. Task parameterized representations allow easy adaptation to new scenes and online observations. However, this approach has been limited to pose-only demonstrations and thus only skills with spatial and temporal features. In this work, we extend the LfD framework to address forceful manipulation skills, which are of great importance for industrial processes such as assembly. For such skills, multi-modal demonstrations including robot end-effector poses, force and torque readings, and operation scene are essential. Our objective is to reproduce such skills reliably according to the demonstrated pose and force profiles within different scenes. The proposed method combines our previous work on task-parameterized optimization and attractor-based impedance control. The learned skill model consists of (i) the attractor model that unifies the pose and force features, and (ii) the stiffness model that optimizes the stiffness for different stages of the skill. Furthermore, an online execution algorithm is proposed to adapt the skill execution to real-time observations of robot poses, measured forces, and changed scenes. We validate this method rigorously on a 7-DoF robot arm over several steps of an E-bike motor assembly process, which require different types of forceful interaction such as insertion, sliding and twisting.

Hierarchical Human-Motion Prediction and Logic-Geometric Programming for Minimal Interference Human-Robot Tasks

In this paper, we tackle the problem of human-robot coordination in sequences of manipulation tasks. Our approach integrates hierarchical human motion prediction with Task and Motion Planning (TAMP). We first devise a hierarchical motion prediction approach by combining Inverse Reinforcement Learning and short-term motion prediction using a Recurrent Neural Network. In a second step, we propose a dynamic version of the TAMP algorithm Logic- Geometric Programming (LGP). Our version of Dynamic LGP, replans periodically to handle the mismatch between the human motion prediction and the actual human behavior. We assess the efficacy of the approach by training the prediction algorithms and testing the framework on the publicly available MoGaze dataset