Fluid Dynamics

Due to the increasing frequency and severity of storm events, driven by the escalation of anthropogenic climate change and urban expansion, there is a requirement for increasingly efficient flood risk management strategies. While Blue-Green Infrastructure (BGI) offers a sustainable solution for managing flood risk, optimal implementation is challenging. To help overcome this challenge, this study presents a novel multi-objective optimisation tool that couples a state-of-the-art hydrodynamic model with a bespoke evolutionary algorithm. The use of a fully dynamic hydrodynamic model enables the tool to accurately evaluate the effectiveness of proposed BGI features with respect to property scale flood vulnerability and hazard analysis. This contrasts with alternative approaches which utilise simplified models, which can only reliably predict inundation extents, thus the proposed optimisation tool provides greater certainty regarding the optimality of the solutions. As a hydrodynamic simulation is required to evaluate each candidate solution, the bespoke evolutionary algorithm is specifically designed to minimise the number of simulations required, ensuring the tool is computationally practical. The effectiveness of the tool in this regard is validated via the derivation of exact convergence measures, for a tractable search space, and via comparisons with benchmark algorithms, for an intractable search space. Compared with traditional design practices, the proposed tool offers an automated approach capable of efficiently exploring a wide range of solutions, providing decision-makers with a set of optimal solutions from which they can make informed investment decisions. The presented methods provide a robust framework for optimising a variety of BGI features in complex urban environments.

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or heuristic weighting of physics residuals and data loss, our approach introduces a learnable blending neuron that dynamically adjusts the relative contribution of each term based on their uncertainties. This mechanism enables stable training and improved generalization without manual tuning. To further enhance efficiency, we integrate a transfer learning strategy that reuses representations from related domains and adapts them to new physical systems with limited data. We validate the framework for the prediction of heat transfer in liquid-metal miniature heat sinks using only 87 CFD datapoints, where the adaptive PINN achieves an error <8%, outperforming shallow neural networks, kernel methods, and physics-only baselines. Our framework provides a general recipe for embedding physics adaptively into neural networks, offering a robust and reproducible approach for data-scarce problems across various scientific domains, including fluid dynamics and material modeling.

Constructing reduced-order models (ROMs) capable of efficiently predicting the evolution of parameter-dependent high-dimensional dynamical systems is crucial in many applications in engineering and applied sciences. A popular class of projection-based ROMs projects the high-dimensional full-order model (FOM) dynamics onto a low-dimensional manifold. These projection-based ROMs approaches often rely on classical model reduction techniques such as proper orthogonal decomposition (POD) or, more recently, on neural network architectures such as autoencoders (AEs). In the case that the ROM is constructed by the POD, one has approximation guaranteed based based on the singular values of the problem at hand. However, POD-based techniques can suffer from slow decay of the singular values in transport- and advection-dominated problems. In contrast to that, AEs allow for better reduction capabilities than the POD, often with the first few modes, but at the price of theoretical considerations. In addition, it is often observed, that AEs exhibits a plateau of the projection error with the increment of the dimension of the trial manifold. In this work, we propose an invertible AE architecture, named inv-AE, that computationally improves upon the stagnation of the reconstruction error typical of traditional AE architectures. Inv-AE is composed of several invertible neural network layers that allows for gradually recovering more information about the FOM solutions the more we increase the dimension of the reduced manifold. Through the application of inv-AE to a 1-dimensional Burgers' equation, a 2-dimensional fluid flow around an obstacle with variable geometry, and a 3-dimensional Korteweg-de Vries, we show that (i) inv-AE mitigates the issue of the characteristic plateau of AEs and (ii) inv-AE can be combined with popular autoencoder-based ROM approaches, e.g., DL-ROM, to improve their accuracy.

While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS). The locality bias of point-wise constraints fails to propagate global information through tortuous channels, causing unstable gradients and conservation violations. To address this, we propose the Multi-scale Weak-form PINN (MUSA-PINN), which reformulates Navier-Stokes equation constraints as integral conservation laws over hierarchical spherical control volumes. We enforce continuity and momentum conservation via flux-balance residuals on control surfaces. Our method utilizes a three-scale subdomain strategy-comprising large volumes for long-range coupling, skeleton-aware meso-scale volumes aligned with transport pathways, and small volumes for local refinement-alongside a two-stage training schedule prioritizing continuity. Experiments on steady incompressible flow in TPMS geometries show MUSA-PINN outperforms state-of-the-art baselines, reducing relative errors by up to 93% and preserving mass conservation.

Underwater robots are widely deployed for ocean exploration and manipulation. Underactuated mechanisms are advantageous in aquatic environments because reducing actuator count lowers motor-leakage risk while introducing inherent mechanical compliance. However, accurate modeling of underwater underactuated and soft robotic systems remains challenging, as it requires identifying high-dimensional structural and hydrodynamic parameters. In this work, we propose a trajectory-driven global optimization framework for unified structural-hydrodynamic modeling of underwater multibody systems. Inspired by the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the proposed approach simultaneously identifies coupled elastic, damping, and distributed hydrodynamic parameters through trajectory-level matching between simulated and experimental motion. This enables high-fidelity reproduction of underactuated mechanisms and compliant soft robotic systems in underwater environments, using as little as a single video recording. We first validate the framework on a link-by-link underactuated multibody mechanism, demonstrating accurate identification of distributed hydrodynamic coefficients, with normalized end-effector position error below 5% across multiple trajectories, initial conditions, and both active-passive and fully passive configurations. The modeling strategy is further validated on an asymmetric octopus-inspired soft arm, confirming its effectiveness for compliant soft robotic systems. Finally, eight identified arms are assembled into a swimming octopus robot, where the unified parameter set enables realistic whole-body behavior without additional retuning. These results demonstrate the scalability and transferability of the proposed structural-hydrodynamic modeling framework across underwater underactuated and soft robotic systems.

Modelling rock-fluid interaction requires solving a set of partial differential equations (PDEs) to predict the flow behaviour and the reactions of the fluid with the rock on the interfaces. Conventional high-fidelity numerical models require a high resolution to obtain reliable results, resulting in huge computational expense. This restricts the applicability of these models for multi-query problems, such as uncertainty quantification and optimisation, which require running numerous scenarios. As a cheaper alternative to high-fidelity models, this work develops eight surrogate models for predicting the fluid flow in porous media. Four of these are reduced-order models (ROM) based on one neural network for compression and another for prediction. The other four are single neural networks with the property of grid-size invariance; a term which we use to refer to image-to-image models that are capable of inferring on computational domains that are larger than those used during training. In addition to the novel grid-size-invariant framework for surrogate models, we compare the predictive performance of UNet and UNet++ architectures, and demonstrate that UNet++ outperforms UNet for surrogate models. Furthermore, we show that the grid-size-invariant approach is a reliable way to reduce memory consumption during training, resulting in good correlation between predicted and ground-truth values and outperforming the ROMs analysed. The application analysed is particularly challenging because fluid-induced rock dissolution results in a non-static solid field and, consequently, it cannot be used to help in adjustments of the future prediction.

Modeling and controlling fluids is critical across science and engineering. Effective flow control can increase lift, reduce drag, enhance mixing, and attenuate noise, potentially unlocking new technologies. Yet controlling fluids is hard: the dynamics are high-dimensional, nonlinear, and multiscale. While reinforcement learning (RL) has recently succeeded in robotics and protein folding through shared benchmarks, fluid dynamics has resisted such progress: each controller is typically tuned to a single geometry and operating point, making results hard to accumulate, transfer, and compare. We introduce HydroGym, a solver-independent RL platform for flow control, and show that standardized infrastructure unlocks transferable control intelligence across flow regimes. HydroGym provides 61+ validated environments spanning laminar to turbulent flows, with systematic Reynolds number progressions up to Re=400,000 and Mach number variations in 2D and 3D. It supports diverse backends, including finite-volume, spectral-element, finite-element, lattice-Boltzmann, and fully differentiable solvers for gradient-enhanced optimization. Across environments, RL agents consistently discover robust control principles, such as boundary-layer manipulation, acoustic-feedback disruption, and wake reorganization, yielding drag reductions exceeding 90% in canonical configurations. Critically, we demonstrate zero-shot transfer: agents trained only on a simplified channel flow achieve 38% friction-drag reduction on an unseen 3D wing section at chord Reynolds number Re=200,000 reducing exploration costs by four orders of magnitude versus direct on-wing optimization. This suggests RL agents uncover essential physics rather than configuration-specific patterns, pointing toward generalizable control. HydroGym offers extensible, scalable community infrastructure for fluid dynamics, machine learning, and control research.

This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained on a single, fixed geometry and then applied for each subdomain solve in the Schwarz method. Results for two-dimensional stenotic arteries of varying shape and length for different inflow conditions are presented and statistically evaluated. One key finding, when using a limited amount of training data, is that incorporating a physics-aware constraint, as, in our case, flow rate conservation, into the USDS improves the prediction accuracy and convergence behavior of the Schwarz method compared to a purely data-driven USDS. As the USDS is a data-driven, inexact subdomain solver, admissible parameter ranges for the geometry and inflow configurations must be defined and tested.

The use of machine learning for modeling, understanding, and controlling large-scale physics systems is quickly gaining in popularity, with examples ranging from electromagnetism over nuclear fusion reactors and magneto-hydrodynamics to fluid mechanics and climate modeling. These systems - governed by partial differential equations - present unique challenges regarding the large number of degrees of freedom and the complex dynamics over many scales both in space and time, and additional measures to improve accuracy and sample efficiency are highly desirable. We present an end-to-end equivariant surrogate model consisting of an equivariant convolutional autoencoder and an equivariant convolutional LSTM using $G$-steerable kernels. As a case study, we consider the three-dimensional Rayleigh-B'enard convection, which describes the buoyancy-driven fluid flow between a heated bottom and a cooled top plate. While the system is E(2)-equivariant in the horizontal plane, the boundary conditions break the translational equivariance in the vertical direction. Our architecture leverages vertically stacked layers of $D_4$-steerable kernels, with additional partial kernel sharing in the vertical direction for further efficiency improvement. We demonstrate significant gains in sample and parameter efficiency, as well as a better scaling to more complex dynamics. The accompanying code is available under https://github.com/FynnFromme/equivariant-rb-forecasting.