Alexey Kornaev

This work addresses uncertainty quantification in machine learning, treating it as a hidden parameter of the model that estimates variance in training data, thereby enhancing the interpretability of predictive models. By predicting both the target value and the certainty of the prediction, combined with deep ensembling to study model uncertainty, the proposed method aims to increase model accuracy. The approach was applied to the well-known problem of Remaining Useful Life (RUL) estimation for turbofan jet engines using NASA’s dataset. The method demonstrated competitive results compared to other commonly used tabular data processing methods, including k-nearest neighbors, support vector machines, decision trees, and their ensembles. The proposed method is based on advanced techniques that leverage uncertainty quantification to improve the reliability and accuracy of RUL predictions.

Despite the fact that the hydrodynamic lubrication is a self-controlled process, the rotor dynamics and energy efficiency in fluid film bearing are often the subject to be improved. We have designed control systems with adaptive PI and DQN-agent based controllers to minimize the rotor oscillations amplitude in a conical fluid film bearing. The design of the bearing allows its axial displacement and thus adjustment of its average clearance. The tests were performed using a simulation model in MATLAB software. The simulation model includes modules of a rigid shaft, a conical bearing, and a control system. The bearing module is based on numerical solution of the generalized Reynolds equation and its nonlinear approximation with fully connected neural networks. The results obtained demonstrate that both the adaptive PI controller and the DQNbased controller reduce the rotor vibrations even when imbalance in the system grows. However, the DQN-based approach provides some additional advantages in the controller designing process as well as in the system performance.

Physics-informed neural networks (PINNs) have demonstrated great promise in solving partial differential equations without labeled data, yet their performance often deteriorates for highly nonlinear systems — particularly steady non-Newtonian flows governed by power-law or yield-stress rheologies. In this work, we present a systematic comparative study of PINN training strategies for Couette flow of pseudoplastic fluids between coaxial cylinders, governed by the Ostwald – de Waele and Herschel – Bulkley constitutive laws. We evaluate three established differential-form PINN variants — baseline (fixed loss weights), curriculum learning, and adaptive loss weighting — and introduce a novel variational PINN (vPINN) derived from the dissipation potential of Herschel – Bulkley fluids. Crucially, the proposed vPINN embeds the principle of minimum dissipation directly into the loss functional via the analytically integrated shear-dependent potential $\Phi(\dot{\gamma}) = q_0^{}\dot{\gamma}^2 + \frac{2q_1^{}\dot{\gamma}^{\,z+1}}{z+1}$, thereby enforcing physics through a variational principle rather than residual minimization. Using an exact analytical solution as ground truth, we benchmark all models on velocity and pressure reconstruction across varying gap geometries $\Bigl($dimensionless parameter $\gamma=\frac{R_1^{}}{R_2^{}-R_1^{}}\Bigr)$. While adaptive weighting improves pressure recovery by $6$–$8\,\%$ (MAE, $L_\infty^{}$, RSD), all differential PINNs exhibit nearly identical — and limited — accuracy for velocity prediction, with no benefit from curriculum scheduling. In contrast, the vPINN achieves a substantial and consistent gain in velocity accuracy: for $\gamma=4.0$, RSD drops from $1.09\,\%$ (all PINNs) to $0.85\,\%$ ($-22\,\%$); for the widest gap ($\gamma=0.67$), RSD falls from $6.0\,\%$ to $4.07\,\%$ ($-32\,\%$). MAE and $L_\infty^{}$ errors decrease by $27\,\%$ and $23\,\%$, respectively. These improvements arise because the variational formulation naturally mitigates spectral bias and avoids ill-conditioned gradients inherent to the highly nonlinear Navier – Stokes equation. The vPINN network also trains approximately twice as fast. Although vPINN currently predicts only velocity (pressure is recovered a posteriori), its consistent accuracy gains — especially where non-Newtonian effects dominate — establish variational PINNs as a compelling, physics-based alternative to residual-based approaches for complex rheological modeling.