arXiv subjects

Francesco Montomoli

Publications and source records attributed to Francesco Montomoli.

3 recordsLinked to original sources

arXiv2024

SeAr PC: Sensitivity Enhanced Arbitrary Polynomial Chaos

This paper presents a method for performing Uncertainty Quantification in high-dimensional uncertain spaces by combining arbitrary polynomial chaos with a recently proposed scheme for sensitivity enhancement (1). Including available sensitivity information offers a way to mitigate the curse of dimensionality in Polynomial Chaos Expansions (PCEs). Coupling the sensitivity enhancement to arbitrary Polynomial Chaos allows the formulation to be extended to a wide range of stochastic processes, including multi-modal, fat-tailed, and truncated probability distributions. In so doing, this work addresses two of the barriers to widespread industrial application of PCEs. The method is demonstrated for a number of synthetic test cases, including an uncertainty analysis of a Finite Element structure, determined using Topology Optimisation, with 306 uncertain inputs. We demonstrate that by exploiting sensitivity information, PCEs can feasibly be applied to such problems and through the Sobol sensitivity indices, can allow a designer to easily visualise the spatial distribution of the contributions to uncertainty in the structure.

math.NA↗

arXiv2023

Investigation of Compressor Cascade Flow Using Physics- Informed Neural Networks with Adaptive Learning Strategy

In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy that mitigates gradient imbalance through incorporating adaptive weights in conjunction with dynamically adjusting learning rate is used during the training process to improve the convergence of PINNs. The performance of PINNs is assessed here by solving both the forward and inverse problems. In the forward problem, by encapsulating the physical relations among relevant variables, PINNs demonstrate their effectiveness in accurately forecasting the compressor's flow field. PINNs also show obvious advantages over the traditional CFD approaches, particularly in scenarios lacking complete boundary conditions, as is often the case in inverse engineering problems. PINNs successfully reconstruct the flow field of the compressor cascade solely based on partial velocity vectors and near-wall pressure information. Furthermore, PINNs show robust performance in the environment of various levels of aleatory uncertainties stemming from labeled data. This research provides evidence that PINNs can offer turbomachinery designers an additional and promising option alongside the current dominant CFD methods.

cs.LG↗

arXiv2023

Surrogate modelling and uncertainty quantification based on multi-fidelity deep neural network

To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is commonly proposed to separately approximate the non-linear and linear correlation between the HF- and LF data. In this paper, a new architecture of multi-fidelity deep neural network (MF-DNN) was proposed where one subnetwork was built to approximate both the non-linear and linear correlation simultaneously. Rather than manually allocating the output weights for the paralleled linear and nonlinear correction networks, the proposed MF-DNN can autonomously learn arbitrary correlation. The prediction accuracy of the proposed MF-DNN was firstly demonstrated by approximating the 1-, 32- and 100-dimensional benchmark functions with either the linear or non-linear correlation. The surrogating modelling results revealed that MF-DNN exhibited excellent approximation capabilities for the test functions. Subsequently, the MF DNN was deployed to simulate the 1-, 32- and 100-dimensional aleatory uncertainty propagation progress with the influence of either the uniform or Gaussian distributions of input uncertainties. The uncertainty quantification (UQ) results validated that the MF-DNN efficiently predicted the probability density distributions of quantities of interest (QoI) as well as the statistical moments without significant compromise of accuracy. MF-DNN was also deployed to model the physical flow of turbine vane LS89. The distributions of isentropic Mach number were well-predicted by MF-DNN based on the 2D Euler flow field and few experimental measurement data points. The proposed MF-DNN should be promising in solving UQ and robust optimization problems in practical engineering applications with multi-fidelity data sources.

physics.comp-ph↗