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Rainald Löhner

Publications and source records attributed to Rainald Löhner.

At least 19 recordsLinked to original sources
arXiv2026

Three-Dimensional Simulation of Flood Propagation at Syabrubesi, Nepal

Three-dimensional flood propagation through the Bhote Koshi--Langtang Khola junction at Syabrubesi, Nepal, is studied using an incompressible free-surface model. The calculation is motivated by the August 2026 flood and examines the passage of an imposed inflow through the local bends and changes in channel width. The Navier--Stokes equations and an interface transport equation are solved on unstructured tetrahedral meshes constructed from pre-event terrain data. For an inlet speed of $10\,\mathrm{m\,s^{-1}}$, the solution indicates surface speeds above $40\,\mathrm{m\,s^{-1}}$. The advancing front spreads across the junction; as the flow develops, water deepens and slows around the bend. Higher speeds persist in the confined upstream and downstream regions.

physics.flu-dyn↗
arXiv2026

Polarization-Induced Beam Bending: Mathematical Model, Discretization, and Algorithm

We study a reduced hydrodynamic formulation of paraxial vector beam propagation in which the beam intensity, optical phase, and spatially-dependent polarization are coupled through a nonlinear dispersive system. While prior analytical work derived a solution for the beam path valid for short propagation distances, a fully resolved numerical treatment of the model over long ranges has not previously been available. Here we present a conservative numerical scheme for the coupled system, combining a finite-volume discretization of the intensity equation with monotone Hamilton--Jacobi (H-J) solvers for the phase dynamics and upwind transport of polarization. The method preserves the nonnegativity of the intensity and remains stable under long-distance propagation. We perform large-scale simulations over propagation distances of tens of meters, while resolving millimeter-scale transverse structure. The numerical results reproduce the analytically predicted and experimentally observed quadratic beam bending at short distances and reveal systematic deviations beyond the asymptotic regime. These deviations arise from nonlinear phase accumulation and dispersive effects captured by the full model but are neglected in the short-distance approximation.

physics.optics↗
arXiv2026

One-Way Thermo-Mechanical Coupled System Identification Using Displacement and Temperature Measurements

Structural system identification in the presence of thermal loads is challenging, as unmeasured or poorly modeled thermal effects can mask or mimic damage, leading to unreliable conclusions. This work presents an optimization-driven, adjoint-based high-fidelity system identification framework for localizing structural weakness and recovering the temperature field in one-way thermo-mechanical coupled structures. The methodology builds upon a standard optimization formulation that minimizes weighted discrepancies between simulated responses and measured data from a sparse displacement and temperature sensor network. To account for thermal effects, two strategies are proposed: a monolithic approach, which simultaneously identifies Young's modulus and temperature distributions, and a partitioned approach, which iteratively couples two inexact sub-problems through a Gauss-Seidel type fixed-point scheme. The proposed approaches are evaluated using two numerical examples -- a Plate With a Hole and a Footbridge model -- under linearly varying and localized thermal fields, and for different sensor layouts. Both approaches successfully recover the Young's modulus and temperature distributions, even when sensor placement does not fully capture the underlying thermal trends. Compared with a constant-temperature assumption and interpolation of the temperature field from sensor data, the proposed approach achieves the most accurate damage localization and temperature reconstruction. The largest gains occur when localized thermal features are poorly sampled by sensors, where interpolation and constant-temperature assumptions underperform. Furthermore, results show that the location of the temperature sensors is as influential as the number of sensors: well-placed sensors substantially improve identification, while additional sensors that miss critical thermal features provide limited benefit.

math.OC↗
arXiv2026

Fisher-Information-Based Sensor Placement for Structural Digital Twins: Analytic Results and Benchmarks

High-fidelity digital twins rely on the accurate assimilation of sensor data into physics-based computational models. In structural applications, such twins aim to identify spatially distributed quantities--such as elementwise weakening fields, material parameters, or effective thermal loads--by minimizing discrepancies between measured and simulated responses subject to the governing equations of structural mechanics. While adjoint-based methods enable efficient gradient computation for these inverse problems, the quality and stability of the resulting estimates depend critically on the choice of sensor locations, measurement types, and directions. This paper develops a rigorous and implementation-ready framework for Fisher-information-based sensor placement in adjoint-based finite-element digital twins. Sensor configurations are evaluated using a D-optimal design criterion derived from a linearization of the measurement map, yielding a statistically meaningful measure of information content. We present matrix-free operator formulas for applying the Jacobian and its adjoint, and hence for computing Fisher-information products $Fv = J^\top R^{-1} Jv$ using only forward and adjoint solves. Building on these operator evaluations, we derive explicit sensitivity expressions for D-optimal sensor design with respect to measurement parameters and discuss practical strategies for evaluating the associated log-determinant objectives. To complement the general framework, we provide analytically tractable sensor placement results for a canonical one-dimensional structural model, clarifying the distinction between detectability and localizability and proving that D-optimal placement of multiple displacement sensors yields approximately uniform spacing.

math.OC↗
arXiv2025

Optimal Boundary Control of Diffusion on Graphs via Linear Programming

We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by edge lengths to preserve geometric fidelity. Boundary potentials act as controls that drive interior fluxes according to a linear network Laplacian. The optimization problem enforces physically meaningful sign and flux-cap constraints at all boundary edges, derived directly from a gradient bound. This yields a finite-dimensional LP whose feasible set is polyhedral, and whose boundedness and solvability follow from simple geometric or algebraic conditions on the network data. We prove that under the absence of negative recession directions--automatically satisfied in the presence of finite box bounds, flux caps, or sign restrictions--the LP admits a global minimizer. Several sufficient conditions guaranteeing boundedness of the feasible region are identified, covering both full-rank and rank-deficient flux maps. The analysis connects classical results such as the Minkowski--Weyl decomposition, Hoffman's bound, and the fundamental theorem of linear programming with modern network-based diffusion modeling. Two large-scale examples illustrate the framework: (i) A typical large stadium in a major modern city, which forms a single connected component with relatively uniform corridor widths, and a (ii) A complex street network emanating from a large, historical city center, which forms a multi-component system.

math.OC↗
arXiv2025

On Techniques for Barely Coupled Multiphysics

A technique to combine codes to solve barely coupled multiphysics problems has been developed. Each field is advanced separately until a stop is triggered. This could be due to a preset time increment, a preset number of timesteps, a preset decrease of residuals, a preset change in unknowns, a preset change in geometry, or any other physically meaningful quantity. The technique allows for a simple implementation in coupled codes using the loose coupling approach. Examples from evaporative cooling of electric motors, a problem that has come to the forefront with the rise of electric propulsion in the aerospace sector (drones and air taxis in particular) shows the viability and accuracy of the proposed procedure.

cs.CE↗
arXiv2024

Adjoint-based Recovery of Thermal Fields from Displacement or Strain Measurements

A finite-element method dependant adjoint-based procedure to determine the temperature field of structures based on measured displacements or strains and a set of standard loads is developed and tested. Given a series of force and deformation measurements, the temperature field is obtained by minimizing the adequately weighted differences between the measured and computed values. Three numerical examples - a Plate With a Hole, a Bridge, and a Hoover Dam example - each with multiple sensors distributed in different configurations, demonstrate the procedure's capabilities. A target temperature distribution is prescribed in all cases, and the displacement sensor data is recorded. The optimization algorithm (here, steepest descent with Barzilai-Borwein step) uses this data to optimize the temperatures such that the same deformation is obtained at the sensor locations. Vertex Morphing is used as a filter to mitigate the ill-conditioning. Results show that the proposed approach can accurately reconstruct the target thermal distribution, especially when more sensors are used. Additionally, it is observed that the sensors do not need to be positioned in the region of interest; the method remains effective as long as the sensors can detect changes related to that area. A comparison with standard spatial interpolation techniques, namely, k-nearest neighbors and ordinary and universal kriging, is performed using temperature sensors in the same configurations. The proposed approach performs remarkably better than the interpolation techniques with a reduction in the root-mean-squared error of up to 38.4%, 94%, and 40%, for the Plate With a Hole, the Bridge, and the Dam examples, respectively.

math.OC↗
arXiv2023

On The Use of Risk Measures in Digital Twins to Identify Weaknesses in Structures

Given measurements from sensors and a set of standard forces, an optimization based approach to identify weakness in structures is introduced. The key novelty lies in letting the load and measurements to be random variables. Subsequently the conditional-value-at-risk (CVaR) is minimized subject to the elasticity equations as constraints. CVaR is a risk measure that leads to minimization of rare and low probability events which the standard expectation cannot. The optimization variable is the (deterministic) strength factor which appears as a coefficient in the elasticity equation, thus making the problem nonconvex. Due to uncertainty, the problem is high dimensional and, due to CVaR, the problem is nonsmooth. An adjoint based approach is developed with quadrature in the random variables. Numerical results are presented in the context of a plate, a large structure with trusses similar to those used in solar arrays or cranes, and a footbridge.

math.OC↗
arXiv2023

High-Fidelity Digital Twins: Detecting and Localizing Weaknesses in Structures

An adjoint-based procedure to determine weaknesses, or, more generally, the material properties of structures is developed and tested. Given a series of load cases and corresponding displacement/strain measurements, the material properties are obtained by minimizing the weighted differences between the measured and computed values. In a subsequent step, techniques to minimize the number of load cases and sensors are proposed and tested. Several examples show the viability, accuracy and efficiency of the proposed methodology and its potential use for high fidelity digital twins.

math.OC↗
arXiv2023

Adjoint-based Determination of Weaknesses in Structures

An adjoint-based procedure to determine weaknesses, or, more generally the material properties of structures is developed and tested. Given a series of force and deformation/strain measurements, the material properties are obtained by minimizing the weighted differences between the measured and computed values. Several examples with truss, plain strain and volume elements show the viability, accuracy and efficiency of the proposed methodology using both displacement and strain measurements. An important finding was that in order to obtain reliable, convergent results the gradient of the cost function has to be smoothed.

math.OC↗
arXiv2022

Neural Network Representation of Time Integrators

Deep neural network (DNN) architectures are constructed that are the exact equivalent of explicit Runge-Kutta schemes for numerical time integration. The network weights and biases are given, i.e., no training is needed. In this way, the only task left for physics-based integrators is the DNN approximation of the right-hand side. This allows to clearly delineate the approximation estimates for right-hand side errors and time integration errors. The architecture required for the integration of a simple mass-damper-stiffness case is included as an example.

math.NA↗
arXiv2022

NINNs: Nudging Induced Neural Networks

New algorithms called nudging induced neural networks (NINNs), to control and improve the accuracy of deep neural networks (DNNs), are introduced. The NINNs framework can be applied to almost all pre-existing DNNs, with forward propagation, with costs comparable to existing DNNs. NINNs work by adding a feedback control term to the forward propagation of the network. The feedback term nudges the neural network towards a desired quantity of interest. NINNs offer multiple advantages, for instance, they lead to higher accuracy when compared with existing data assimilation algorithms such as nudging. Rigorous convergence analysis is established for NINNs. The algorithmic and theoretical findings are illustrated on examples from data assimilation and chemically reacting flows.

cs.LG↗
arXiv2022

Deep Neural Nets with Fixed Bias Configuration

For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in the millions even for small networks) of equivalent optimal solutions in the parameter space. To the best of our knowledge, this observation is absent in the literature. In order to narrow down the parameter search space, a novel technique is introduced in order to fix the bias vector configurations to be monotonically increasing. This is achieved by augmenting a typical learning problem with inequality constraints on the bias vectors in each layer. A Moreau-Yosida regularization based algorithm is proposed to handle these inequality constraints and a theoretical convergence of the this algorithm is established. Applications of the proposed approach to standard trigonometric functions and more challenging stiff ordinary differential equations arising in chemically reacting ows clearly illustrate the benefits of the proposed approach.

math.OC↗
arXiv2022

A Deterministic Pathogen Transmission Model Based on High-Fidelity Physics

A deterministic pathogen transmission model based on high-fidelity physics has been developed. The model combines computational fluid dynamics and computational crowd dynamics in order to be able to provide accurate tracing of viral matter that is exhaled, transmitted and inhaled via aerosols. The examples shown indicate that even with modest computing resources, the propagation and transmission of viral matter can be simulated for relatively large areas with thousands of square meters, hundreds of pedestrians and several minutes of physical time. The results obtained and insights gained from these simulations can be used to inform global pandemic propagation models, increasing substantially their accuracy.

math.NA↗
arXiv2021

Data Assimilation with Deep Neural Nets Informed by Nudging

The nudging data assimilation algorithm is a powerful tool used to forecast phenomena of interest given incomplete and noisy observations. Machine learning is becoming increasingly popular in data assimilation given its ease of computation and forecasting ability. This work proposes a new approach to data assimilation via machine learning where Deep Neural Networks (DNNs) are being taught the nudging algorithm. The accuracy of the proposed DNN based algorithm is comparable to the nudging algorithm and it is confirmed by the Lorenz 63 and Lorenz 96 numerical examples. The key advantage of the proposed approach is the fact that, once trained, DNNs are cheap to evaluate in comparison to nudging where typically differential equations are needed to be solved. Standard exponential type approximation results are established for the Lorenz 63 model for both the continuous and discrete in time models. These results can be directly coupled with estimates for DNNs (whenever available), to derive the overall approximation error estimates of the proposed algorithm.

math.NA↗
arXiv2021

Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows

Chemically reacting flows are common in engineering, such as hypersonic flow, combustion, explosions, manufacturing processes and environmental assessments. For combustion, the number of reactions can be significant (over 100) and due to the very large CPU requirements of chemical reactions (over 99%) a large number of flow and combustion problems are presently beyond the capabilities of even the largest supercomputers. Motivated by this, novel Deep Neural Networks (DNNs) are introduced to approximate stiff ODEs. Two approaches are compared, i.e., either learn the solution or the derivative of the solution to these ODEs. These DNNs are applied to multiple species and reactions common in chemically reacting flows. Experimental results show that it is helpful to account for the physical properties of species while designing DNNs. The proposed approach is shown to generalize well.

cs.LG↗
arXiv2020

High Fidelity Modeling of Aerosol Pathogen Propagation in Built Environments with Moving Pedestrians

A high fidelity model for the propagation of pathogens via aerosols in the presence of moving pedestrians is proposed. The key idea is the tight coupling of computational fluid dynamics and computational crowd dynamics in order to capture the emission, transport and inhalation of pathogen loads in space and time. An example simulating pathogen propagation in a narrow corridor with moving pedestrians clearly shows the considerable effect that pedestrian motion has on airflow, and hence on pathogen propagation and potential infectivity.

physics.soc-ph↗