Aniket Bera

Hrishikesh Viswanath, Juanwu Lu, S. Talha Bukhari et al.

Offline goal-conditioned reinforcement learning (GCRL) learns goal-conditioned policies from static pre-collected datasets. However, accurate value estimation remains a challenge due to the limited coverage of the state-action space. Recent physics-informed approaches have sought to address this by imposing physical and geometric constraints on the value function through regularization defined over first-order partial differential equations (PDEs), such as the Eikonal equation. However, these formulations can often be ill-posed in complex, high-dimensional environments. In this work, we propose a physics-informed regularization derived from the viscosity solution of the Hamilton-Jacobi-Bellman (HJB) equation. By providing a physics-based inductive bias, our approach grounds the learning process in optimal control theory, explicitly regularizing and bounding updates during value iterations. Furthermore, we leverage the Feynman-Kac theorem to recast the PDE solution as an expectation, enabling a tractable Monte Carlo estimation of the objective that avoids numerical instability in higher-order gradients. Experiments demonstrate that our method improves geometric consistency, making it broadly applicable to navigation and high-dimensional, complex manipulation tasks. Open-source codes are available at https://github.com/HrishikeshVish/phys-fk-value-GCRL.

Hrishikesh Viswanath, Hong Chul Nam, Xi Deng et al.

Training neural PDE solvers is often bottlenecked by expensive data generation or unstable physics-informed neural network (PINN) involving challenging optimization landscapes due to higher-order derivatives. To tackle this issue, we propose an alternative approach using Monte Carlo approaches to estimate the solution to the PDE as a stochastic process for weak supervision during training. Leveraging the Walk-on-Spheres method, we introduce a learning scheme called \emph{Walk-on-Spheres Neural Operator (WoS-NO)} which uses weak supervision from WoS to train any given neural operator. We propose to amortize the cost of Monte Carlo walks across the distribution of PDE instances using stochastic representations from the WoS algorithm to generate cheap, noisy, estimates of the PDE solution during training. This is formulated into a data-free physics-informed objective where a neural operator is trained to regress against these weak supervisions, allowing the operator to learn a generalized solution map for an entire family of PDEs. This strategy does not require expensive pre-computed datasets, avoids computing higher-order derivatives for loss functions that are memory-intensive and unstable, and demonstrates zero-shot generalization to novel PDE parameters and domains. Experiments show that for the same number of training steps, our method exhibits up to 8.75$\times$ improvement in $L_2$-error compared to standard physics-informed training schemes, up to 6.31$\times$ improvement in training speed, and reductions of up to 2.97$\times$ in GPU memory consumption. We present the code at https://github.com/neuraloperator/WoS-NO

Apoorva Vashisth, Manav Kulshrestha, Pranav Bakshi et al.

Visual navigation typically assumes the existence of at least one obstacle-free path between start and goal, which must be discovered/planned by the robot. However, in real-world scenarios, such as home environments and warehouses, clutter can block all routes. Targeted at such cases, we introduce the Lifelong Interactive Navigation problem, where a mobile robot with manipulation abilities can move clutter to forge its own path to complete sequential object- placement tasks - each involving placing an given object (eg. Alarm clock, Pillow) onto a target object (eg. Dining table, Desk, Bed). To address this lifelong setting - where effects of environment changes accumulate and have long-term effects - we propose an LLM-driven, constraint-based planning framework with active perception. Our framework allows the LLM to reason over a structured scene graph of discovered objects and obstacles, deciding which object to move, where to place it, and where to look next to discover task-relevant information. This coupling of reasoning and active perception allows the agent to explore the regions expected to contribute to task completion rather than exhaustively mapping the environment. A standard motion planner then executes the corresponding navigate-pick-place, or detour sequence, ensuring reliable low-level control. Evaluated in physics-enabled ProcTHOR-10k simulator, our approach outperforms non-learning and learning-based baselines. We further demonstrate our approach qualitatively on real-world hardware.