An T. Le

Joe Watson, Chen Song, Oliver Weeger et al. · cambridge

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.

An T. Le, Kay Hansel, Jan Peters et al.

We present hierarchical policy blending as optimal transport (HiPBOT). HiPBOT hierarchically adjusts the weights of low-level reactive expert policies of different agents by adding a look-ahead planning layer on the parameter space. The high-level planner renders policy blending as unbalanced optimal transport consolidating the scaling of the underlying Riemannian motion policies. As a result, HiPBOT effectively decides the priorities between expert policies and agents, ensuring the task's success and guaranteeing safety. Experimental results in several application scenarios, from low-dimensional navigation to high-dimensional whole-body control, show the efficacy and efficiency of HiPBOT. Our method outperforms state-of-the-art baselines -- either adopting probabilistic inference or defining 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

Julen Urain, An T. Le, Alexander Lambert et al.

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.

Joao Carvalho, An T. Le, Mark Baierl et al.

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.

Duy M. H. Nguyen, An T. Le, Trung Q. Nguyen et al.

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.

Duc Minh Nguyen, Bao-Ngoc Dao, Tung M. Luu et al.

Diffusion-based Vision-Language-Action (VLA) policies enable strong generalization in robotic manipulation, but remain sensitive to spurious visual correlations and noisy action generation, leading to brittle behavior under perturbations. We introduce Selected Diffusion Noise (SDN), a simple, training-free test-time method that improves both robustness and success rate by leveraging the diffusion noise space as a controllable degree of freedom. SDN dynamically samples noise vectors that are maximally separated from a reference set to mitigate reliance on spurious cues, while selecting candidates that yield more coherent action trajectories. This dual objective encourages stable behavior even under object-masked observations and reduces action jitter without modifying model parameters. We evaluate SDN on two simulation benchmarks (Google Robot, Widow-X) and two real-world robotic datasets across multiple VLA policies, including pi_0, Groot-N1.5, and Groot-N1.6. SDN consistently improves success rates by +8% in simulation and +10% in real-world settings, while producing smoother and more stable actions. Our results highlight that diffusion noise selection can serve as an effective and general mechanism for enhancing VLA policies at test time.

Minh-Loi Nguyen, Nghiem Tuong Diep, Hung Khang Nguyen et al.

Recent advances in robot world models enable synthetic video generation for embodied prediction and planning. However, evaluating these videos is challenging: visually realistic outputs often violate physical laws, temporal consistency, or task logic, while conventional metrics and monolithic Vision-Language Model (VLM) judges fail to generalize or provide precise diagnostic value. We present RoboGaze, a training-free, multi-agent VLM framework that provides structured, interpretable evaluation for generated robot-manipulation videos. Given a task instruction and video, RoboGaze operates via a three-stage pipeline: task-scene grounding, dimension-specific specialist routing, and critic-based verification. It outputs temporally localized glitch reports categorized under a novel 6-dimension, 30-type robotics-specific taxonomy. To benchmark RoboGaze, we introduce a human-validated dataset of 382 clips spanning simulated and real-world multi-view manipulation. Evaluating eight open-source and proprietary VLM backbones, RoboGaze dramatically outperforms zero-shot baselines, improving description-F1 by up to +43 points and temporal alignment (F1 x IoU) by up to +37 points, closing approximately 85% of the gap to the human ceiling. Furthermore, its critic verifier mitigates the "cry-wolf" false-positive flaw of standard VLMs, lifting clean-clip accuracy from under 25% to over 80%. RoboGaze offers a scalable, highly interpretable diagnostic tool for the rigorous evaluation of robot world models.

Trong-Bao Ho, Quang-Tan Nguyen, Thien-Loc Ha et al.

Action chunking enables robot policies to produce temporally coherent behavior, but generating multi-step action sequences with flow-based policies incurs latency that is incompatible with real-time control. Under asynchronous execution, the robot continues executing the current chunk while the next one is generated, causing even minor delays to create inconsistencies at chunk boundaries. Existing methods address this problem by steering generation toward the already executed action prefix. We instead show that prefix consistency can be achieved by selecting an appropriate initial noise before generation begins, allowing the unmodified flow ODE to produce a coherent next chunk. This reframes asynchronous inference as a noise selection problem rather than a trajectory steering problem. We introduce \textbf{PAINT}, a training-free method that finds this noise via backward Euler inversion and constructs the final chunk through a repainting rule. In summary, \texttt{PAINT} requires no gradients, retraining, or policy modification; yet it improves execution consistency and task performance across \textit{12 simulated benchmarks} and \textit{6 real-world manipulation tasks} spanning single-arm, bimanual, and humanoid embodiments. Website: ~\href{https://paint-action-chunking.github.io}{\texttt{https://paint-action-chunking.github.io}}.

Joao Carvalho, An T. Le, Philipp Jahr et al.

Grasping objects successfully from a single-view camera is crucial in many robot manipulation tasks. An approach to solve this problem is to leverage simulation to create large datasets of pairs of objects and grasp poses, and then learn a conditional generative model that can be prompted quickly during deployment. However, the grasp pose data is highly multimodal since there are several ways to grasp an object. Hence, in this work, we learn a grasp generative model with diffusion models to sample candidate grasp poses given a partial point cloud of an object. A novel aspect of our method is to consider diffusion in the manifold space of rotations and to propose a collision-avoidance cost guidance to improve the grasp success rate during inference. To accelerate grasp sampling we use recent techniques from the diffusion literature to achieve faster inference times. We show in simulation and real-world experiments that our approach can grasp several objects from raw depth images with $90\%$ success rate and benchmark it against several baselines.

An T. Le, Kay Hansel, João Carvalho et al.

Batch planning is increasingly necessary to quickly produce diverse and quality motion plans for downstream learning applications, such as distillation and imitation learning. This paper presents Global Tensor Motion Planning (GTMP) -- a sampling-based motion planning algorithm comprising only tensor operations. We introduce a novel discretization structure represented as a random multipartite graph, enabling efficient vectorized sampling, collision checking, and search. We provide a theoretical investigation showing that GTMP exhibits probabilistic completeness while supporting modern GPU/TPU. Additionally, by incorporating smooth structures into the multipartite graph, GTMP directly plans smooth splines without requiring gradient-based optimization. Experiments on lidar-scanned occupancy maps and the MotionBenchMarker dataset demonstrate GTMP's computation efficiency in batch planning compared to baselines, underscoring GTMP's potential as a robust, scalable planner for diverse applications and large-scale robot learning tasks.

Duy M. H. Nguyen, Nina Lukashina, Tai Nguyen et al.

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 $\mathrm{E}$(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 Fused Gromov-Wasserstein Barycenter problem and the use of an efficient conformer generation method based on distance geometry. We show that the proposed aggregation mechanism is $\mathrm{E}$(3) invariant and propose an efficient GPU implementation. Moreover, we demonstrate that the aggregation mechanism helps to significantly outperform state-of-the-art molecule property prediction methods on established datasets.

Thien-Loc Ha, Quang-Tan Nguyen, Trong-Bao Ho et al.

Vision-Language-Action (VLA) models have emerged as a powerful paradigm for generalist robot manipulation, yet they lack geometric inductive biases: policies trained at specific orientations require substantially more data to generalize across rotational configurations. We present \textsc{EquiVLA}, the first general framework for end-to-end $\mathrm{SO}(2)$-equivariant VLA models, applicable to any architecture coupling a frozen vision-language backbone with a flow-matching Diffusion Transformer action head. \textsc{EquiVLA} introduces \textsc{EquiPerceptor}, which produces approximately $\mathrm{SO}(2)$-equivariant visual representations from frozen ViT features; and \textsc{EquiActor}, an exactly $\mathrm{SO}(2)$-equivariant flow-matching Diffusion Transformer action head. Together, they establish an approximate $\mathrm{SO}(2)$ equivariance chain from camera observations to predicted action sequences. Instantiated on GR00T~N1.5 and evaluated across four LIBERO suites, CALVIN ABCD$\to$D, and five real-robot tasks on Mobile ALOHA, \textsc{EquiVLA} achieves $92.6\%$ average success on LIBERO (vs. $78.1\%$ baseline), an average sequence length of $4.03$ on CALVIN (vs. $3.45$), and improves real-robot success from $54\%$ to $72\%$.

Duc Minh Nguyen, Nghiem Tuong Diep, Binh Gia Nguyen et al.

Vision-Language-Action (VLA) models enable general-purpose robotic control via large-scale multimodal pretraining, yet their effectiveness under few-shot imitation learning remains limited. We conduct a systematic stress test of state-of-the-art VLA models and show that performance degrades sharply as demonstrations are reduced, revealing a key weakness of existing adaptation strategies. To address this, we introduce FOCA, a future-oriented conditioning framework for data-efficient VLA adaptation. FOCA combines explicit prediction of task-grounded future interaction embeddings with implicit alignment to future goal observations, enabling long-horizon reasoning in latent space without pixel-level prediction. This formulation naturally supports action-free co-training with synthetic videos from video world models and can be interpreted as learning a future-conditioned value-like representation. Extensive experiments demonstrate FOCA achieves 95.7% success with 20 demonstrations on LIBERO, improves 7-12% on RoboCasa, and delivers up to 26% absolute gains on real robots, establishing a new state of the art in few-shot VLA adaptation.

Magnus Dierking, Joao Carvalho, An Thai Le et al.

Sampling-based Model Predictive Control (SMPC) is a promising strategy for contact-rich robotic manipulation, combining gradient-free optimization with massively parallel GPU simulation. Yet, most prior work relies on simplified dynamics or remains confined to simulation. We present an MPC framework that leverages JAX for large-scale parallelization and efficient computation, coupled with the high-fidelity MuJoCo MJX simulator, and deploy it on a Franka Research 3 executing the Push-T manipulation task through a complete real-to-sim-to-real pipeline. The MTP variant with structured global sampling outperforms unimodal baselines such as CEM, MPPI, and PS across tasks that require mode switching, both in simulation and on hardware. Furthermore, we evaluate online domain randomization within the MPC sample budget, showing that contact-initiation parameters yield interpretable adaptation signals, whereas global physics parameters provide feedback that is too weak for reliable exploitation at typical replanning frequencies. These findings highlight key challenges for sampling-based MPC in contact-rich manipulation-contact sensitivity, tight compute budgets, and the difficulty of obtaining informative domain-randomization signals in real time.

Hung Nguyen, An Le, Runfa Li et al.

3D Gaussian Splatting has emerged as a powerful approach in novel view synthesis, delivering rapid training and rendering but at the cost of an ever-growing set of Gaussian primitives that strains memory and bandwidth. We introduce AutoOpti3DGS, a training-time framework that automatically restrains Gaussian proliferation without sacrificing visual fidelity. The key idea is to feed the input images to a sequence of learnable Forward and Inverse Discrete Wavelet Transforms, where low-pass filters are kept fixed, high-pass filters are learnable and initialized to zero, and an auxiliary orthogonality loss gradually activates fine frequencies. This wavelet-driven, coarse-to-fine process delays the formation of redundant fine Gaussians, allowing 3DGS to capture global structure first and refine detail only when necessary. Through extensive experiments, AutoOpti3DGS requires just a single filter learning-rate hyper-parameter, integrates seamlessly with existing efficient 3DGS frameworks, and consistently produces sparser scene representations more compatible with memory or storage-constrained hardware.

An Le, Hung Nguyen, Sungbal Seo et al.

This work introduces a novel biorthogonal tunable wavelet unit constructed using a lifting scheme that relaxes both the orthogonality and equal filter length constraints, providing greater flexibility in filter design. The proposed unit enhances convolution, pooling, and downsampling operations, leading to improved image classification and anomaly detection in convolutional neural networks (CNN). When integrated into an 18-layer residual neural network (ResNet-18), the approach improved classification accuracy on CIFAR-10 by 2.12% and on the Describable Textures Dataset (DTD) by 9.73%, demonstrating its effectiveness in capturing fine-grained details. Similar improvements were observed in ResNet-34. For anomaly detection in the hazelnut category of the MVTec Anomaly Detection dataset, the proposed method achieved competitive and wellbalanced performance in both segmentation and detection tasks, outperforming existing approaches in terms of accuracy and robustness.

Hung Nguyen, An Le, Truong Nguyen

3D Gaussian Splatting (3DGS) has emerged as a powerful approach for novel view synthesis. However, the number of Gaussian primitives often grows substantially during training as finer scene details are reconstructed, leading to increased memory and storage costs. Recent coarse-to-fine strategies regulate Gaussian growth by modulating the frequency content of the ground-truth images. In particular, AutoOpti3DGS employs the learnable Discrete Wavelet Transform (DWT) to enable data-adaptive frequency modulation. Nevertheless, its modulation depth is limited by the 1-level DWT, and jointly optimizing wavelet regularization with 3D reconstruction introduces gradient competition that promotes excessive Gaussian densification. In this paper, we propose a multi-level DWT-based frequency modulation framework for 3DGS. By recursively decomposing the low-frequency subband, we construct a deeper curriculum that provides progressively coarser supervision during early training, consistently reducing Gaussian counts. Furthermore, we show that the modulation can be performed using only a single scaling parameter, rather than learning the full 2-tap high-pass filter. Experimental results on standard benchmarks demonstrate that our method further reduces Gaussian counts while maintaining competitive rendering quality.

An T. Le, Khai Nguyen, Minh Nhat Vu et al.

Sampling-based model predictive control (MPC) offers strong performance in nonlinear and contact-rich robotic tasks, yet often suffers from poor exploration due to locally greedy sampling schemes. We propose \emph{Model Tensor Planning} (MTP), a novel sampling-based MPC framework that introduces high-entropy control trajectory generation through structured tensor sampling. By sampling over randomized multipartite graphs and interpolating control trajectories with B-splines and Akima splines, MTP ensures smooth and globally diverse control candidates. We further propose a simple $β$-mixing strategy that blends local exploitative and global exploratory samples within the modified Cross-Entropy Method (CEM) update, balancing control refinement and exploration. Theoretically, we show that MTP achieves asymptotic path coverage and maximum entropy in the control trajectory space in the limit of infinite tensor depth and width. Our implementation is fully vectorized using JAX and compatible with MuJoCo XLA, supporting \emph{Just-in-time} (JIT) compilation and batched rollouts for real-time control with online domain randomization. Through experiments on various challenging robotic tasks, ranging from dexterous in-hand manipulation to humanoid locomotion, we demonstrate that MTP outperforms standard MPC and evolutionary strategy baselines in task success and control robustness. Design and sensitivity ablations confirm the effectiveness of MTP tensor sampling structure, spline interpolation choices, and mixing strategy. Altogether, MTP offers a scalable framework for robust exploration in model-based planning and control.

Jiayun Li, Kay Pompetzki, An Thai Le et al.

Gaussian Process Motion Planning (GPMP) is a widely used framework for generating smooth trajectories within a limited compute time--an essential requirement in many robotic applications. However, traditional GPMP approaches often struggle with enforcing hard nonlinear constraints and rely on Maximum a Posteriori (MAP) solutions that disregard the full Bayesian posterior. This limits planning diversity and ultimately hampers decision-making. Recent efforts to integrate Stein Variational Gradient Descent (SVGD) into motion planning have shown promise in handling complex constraints. Nonetheless, these methods still face persistent challenges, such as difficulties in strictly enforcing constraints and inefficiencies when the probabilistic inference problem is poorly conditioned. To address these issues, we propose a novel constrained Stein Variational Gaussian Process Motion Planning (cSGPMP) framework, incorporating a GPMP prior specifically designed for trajectory optimization under hard constraints. Our approach improves the efficiency of particle-based inference while explicitly handling nonlinear constraints. This advancement significantly broadens the applicability of GPMP to motion planning scenarios demanding robust Bayesian inference, strict constraint adherence, and computational efficiency within a limited time. We validate our method on standard benchmarks, achieving an average success rate of 98.57% across 350 planning tasks, significantly outperforming competitive baselines. This demonstrates the ability of our method to discover and use diverse trajectory modes, enhancing flexibility and adaptability in complex environments, and delivering significant improvements over standard baselines without incurring major computational costs.

Georgia Chalvatzaki, Ali Younes, Daljeet Nandha et al.

Long-horizon task planning is essential for the development of intelligent assistive and service robots. In this work, we investigate the applicability of a smaller class of large language models (LLMs), specifically GPT-2, in robotic task planning by learning to decompose tasks into subgoal specifications for a planner to execute sequentially. Our method grounds the input of the LLM on the domain that is represented as a scene graph, enabling it to translate human requests into executable robot plans, thereby learning to reason over long-horizon tasks, as encountered in the ALFRED benchmark. We compare our approach with classical planning and baseline methods to examine the applicability and generalizability of LLM-based planners. Our findings suggest that the knowledge stored in an LLM can be effectively grounded to perform long-horizon task planning, demonstrating the promising potential for the future application of neuro-symbolic planning methods in robotics.

An T. Le, Meng Guo, Niels van Duijkeren et al.

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.

An T. Le, Philipp Kratzer, Simon Hagenmayer et al.

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.