Boyuan Deng

Boyuan Deng, Kshitiz Upadhyay, Michael Shields

The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $κ^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP) regression supplies this by returning a posterior over the solution, yet operator-conditioned formulations have been developed almost exclusively for real-valued fields. We extend operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning. The construction admits a family of priors, from a proper diagonal prior to coregionalized and multiscale variants, and conditions on PDE residuals and boundary traces. On benchmark problems in one to three dimensions, the solver is competitive with finite-difference and neural-network baselines at a far smaller interior-constraint budget. Unlike those deterministic baselines, it returns a posterior over the complex wavefield rather than a point estimate. Applied to \textit{in vivo} brain magnetic resonance elastography, a proper multiscale prior reconstructs the shear curl field to a correlation of $0.77$ with measurement, above a $0.75$ target. The gain arises from the multiscale kernel rather than from real--imaginary coupling. We further identify a low-frequency accuracy ceiling set by model mismatch and a posterior uncertainty that is not yet calibrated. Calibrated uncertainty therefore emerges as the central next step for probabilistic wavefield inference in dissipative media.

Boyuan Deng, Luca Rossini, Jin Wang et al.

Adaptive recovery from fall incidents are essential skills for the practical deployment of wheeled-legged robots, which uniquely combine the agility of legs with the speed of wheels for rapid recovery. However, traditional methods relying on preplanned recovery motions, simplified dynamics or sparse rewards often fail to produce robust recovery policies. This paper presents a learning-based framework integrating Episode-based Dynamic Reward Shaping and curriculum learning, which dynamically balances exploration of diverse recovery maneuvers with precise posture refinement. An asymmetric actor-critic architecture accelerates training by leveraging privileged information in simulation, while noise-injected observations enhance robustness against uncertainties. We further demonstrate that synergistic wheel-leg coordination reduces joint torque consumption by 15.8% and 26.2% and improves stabilization through energy transfer mechanisms. Extensive evaluations on two distinct quadruped platforms achieve recovery success rates up to 99.1% and 97.8% without platform-specific tuning. The supplementary material is available at https://boyuandeng.github.io/L2R-WheelLegCoordination/