Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots

While physics-informed neural networks (PINNs) have shown strong potential for process modeling, physical equations are only enforced as soft constraints during training, and thus, they do not guarantee constraint satisfaction at inference. We propose a framework, called piecewise-linear Karush--Kuhn--Tucker hard-constrained PINNs (PL-KKT-hPINNs), that strictly enforces nonlinear equality constraints through piecewise-linear projection. This extends the KKT-hPINN framewor, which exactly enforces linear equalities through the Karush--Kuhn--Tucker (KKT) conditions associated with orthogonally projecting neural network outputs onto the constraint feasible region. The method is demonstrated on a continuous stirred-tank reactor (CSTR) case study for both one and two inputs. Results show that PL-KKT-hPINN preserves predictive accuracy comparable to that of a standard neural network while achieving substantially lower constraint violations. In addition, the proposed model shows improved robustness in low-data regimes, yielding lower RMSE than the unconstrained neural network for limited training sample sizes. These results demonstrate that PL-KKT-hPINN provides a computationally efficient and physically consistent framework for surrogate modeling of nonlinear chemical engineering systems.

Predicting how deformable objects evolve under robotic manipulation is a longstanding challenge. Existing approaches typically rely on per-object optimization to fit material parameters, which can be slow and cannot generalize, while end-to-end learned alternatives extrapolate poorly and often violate basic physical structure. We present PhysCoRe, a physics-corrected residual world model that couples a differentiable Material Point Method (MPM) simulator with two feed-forward neural networks. A material refinement module, Material from Motion (MfM), infers per-particle elasticity from visual observations, grounding the simulator in object-specific physics. A residual correction module, Residual from Dynamics (RfD), learns the discrepancy and predicts corrections to the simulator's internal dynamics, absorbing systematic biases that the analytical model cannot capture. This design also supports online material identification on novel objects. MfM adapts from limited interactions, and its predictive uncertainty steers further exploration toward the regions where its estimate is least confident. Experiments on real deformable-object manipulation sequences show that PhysCoRe outperforms state-of-the-art baselines in prediction accuracy, and that its predicted confidence forms a reliable distribution across the object's geometry, providing a natural signal for future confidence-guided exploration.

Accurate dynamics modeling of Brushless DC (BLDC) motors is fundamental to high-performance robotic joint control. This paper presents a Physics-Informed Neural Network (PINN) with a deep residual (ResNet) backbone that learns a continuous-time surrogate of the full six-state BLDC motor dynamics. Given simulation time, applied three-phase voltages, and excitation parameters as inputs, the network directly predicts all motor state variables -- rotor angle, angular velocity, three-phase currents, and winding temperature -- while simultaneously satisfying the governing electromechanical and thermal ODEs through a composite physics-data loss. A curriculum scheduling strategy gradually activates the physics penalty to prevent premature convergence. Training runs are completed in under two minutes on a standard CPU. Crucially, once trained, PINN inference achieves latencies of 0.1--22, mu s per query, up to 118x faster than conventional ODE solvers, making it suitable for real-time observer and control applications.