This work introduces a data-driven, non-intrusive reduced-order modeling (ROM) framework that leverages Optimal Transport (OT) for multi-fidelity and parametric problems in two-phase flows modeling. Building upon the success of displacement interpolation for data augmentation in handling nonlinear dynamics, we extend its application to more complex and practical scenarios. The framework is designed to correct a computationally inexpensive low-fidelity (LF) model to match an accurate high-fidelity (HF) one by capturing its temporal evolution via displacement interpolation while preserving the problem’s physical consistency. The framework is further extended to address systems dependent on a physical parameter, for which we construct a surrogate model using a hierarchical, two-level interpolation strategy. First, it creates synthetic HF checkpoints via displacement interpolation in the parameter space. Second, the residual between these synthetic HF checkpoints and a true LF solution is interpolated in the time domain using the multi-fidelity OT-based methodology. This strategy provides a robust and efficient way to explore the parameter space and to obtain a refined description of the dynamical system. The potential of the method is discussed in the context of complex and computationally expensive diffused-interface methods for two-phase flow simulations, which are characterized by moving interfaces and nonlinear evolution, and challenging to be dealt with traditional ROM techniques.
We analyze fractional phase-transition energies with periodic heterogeneities at the critical H-1/2 scaling. We prove that the Gamma-limit is a sharp-interface functional whose surface energy density combines homogenization and averaging effects. The resulting coefficient is a weighted combination of the minimum and the mean of the oscillatory parameter, reflecting the coexistence of multiple interaction scales. This behavior is specific to the critical regime and differs from the case s > 1/2.
We propose a reinforcement learning (RL) framework for the dynamic selection of the filter parameter in Evolve–Filter (EF) regularization strategies for incompressible turbulent flows. Instead of prescribing the filter radius heuristically, the RL agent learns to adaptively control the filtering intensity in time, balancing numerical stability and physical accuracy.The methodology is assessed on two benchmark problems with fundamentally different dynamics: flow past a cylinder and decaying homogeneous turbulence. Both reference-guided and reference-free reward formulations are investigated. In the reference-guided data-driven setting, the agent is trained using direct numerical simulation (DNS) data over a limited time window and then evaluated in time extrapolation and in unseen simulation settings, e.g. Reynolds number and time step size. In the reference-free data-free setting, the reward relies exclusively on physics-based quantities, without access to reference solutions, i.e., completely eliminating the computational costs related to DNS simulations.Results show that the proposed RL-EF strategies prevent numerical blow-up while avoiding the excessive dissipation typical of standard EF approaches based on a fixed Kolmogorov length scale. The learned policies accurately reproduce the relevant flow dynamics across scales, preserving the correct balance between large-scale structures and small-scale dissipation. Notably, the reference-free reward achieves performance comparable to the reference-guided approach, demonstrating that stable and spectrally consistent filtering strategies can be learned even without or with limited DNS data (hybrid RL-EF approach), drastically reducing the computational costs of the training phase.The proposed framework provides a robust and flexible alternative to manually tune regularization parameters, enabling adaptive, physically consistent control of filtering in two-dimensional convection-dominated flow simulations.
The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN’s major difficulties for coupling with external forward solvers arise from the inability to access the discretized form (Finite difference, finite volume, finite element, etc.) of the governing equation directly through the network and to include them in its computational graph. This poses a significant challenge to conventional automatic-differentiation-based derivative computation of physics-based loss terms concerning the neural network hyperparameters if gradient-based optimization techniques are adopted. Therefore, we propose modifying the physics-based loss term to account for the residual arising from the external solver and to compute the derivative required for the optimization machinery. The proposed methodologies are demonstrated on benchmark full-order and reduced-order systems.
The origin of obscuration in active galactic nuclei (AGN) is still a matter of contention. It is unclear whether obscured AGN are primarily due to line-of-sight effects (Orientation model), a transitory, dust-enshrouded phase in galaxy evolution (Evolution models), or a combination of both. The role of an inner torus around the central supermassive black hole also remains unclear in pure Evolution models. We use cosmological semi-analytic models and semi-empirical prescriptions to explore obscuration effects in AGN at cosmic noon, in the range 1 < z < 3. We consider a realistic object-by-object modelling of AGN evolution including different AGN light curves (LCs) composed of phases of varying levels of obscuration, usually (but not uniquely) with a larger degree of obscuration before the peak of AGN activity, mimicking the possible clearing effects of strong AGN feedback. Evolution models characterized by AGN LCs with relatively short pre-peak obscured phases followed by more extended optical/ultraviolet (UV) visible post-peak phases, struggle to reproduce the high fraction of obscured AGN at z similar to 2-3 inferred from X-ray surveys. Evolution models characterized by AGN LCs with sharp post-peak declines or persistent or multiple obscuration phases are more successful, although they still face challenges in reproducing the steady drop in the fractions of obscured AGN with increasing luminosity measured by some groups. Invoking a fine-tuning in the input LCs, with more luminous AGN defined by longer optical/UV visible windows, can improve the match to the decreasing fractions of obscured AGN with luminosity. Alternatively, a long-lived central torus-like component, with thickness decreasing with increasing AGN power, naturally boosts the luminosity-dependent fractions of obscured AGN, suggesting that small-scale orientation effects may still represent a key component even in Evolution models. We also find that in our models major mergers and starbursts, when considered in isolation, fall short in accounting for the large fractions of highly obscured faint AGN detected at cosmic noon.
