Multi-fidelity surrogate modeling using long short-term memory networks

Conti, Paolo; Guo, Mengwu; Manzoni, Andrea; Hesthaven, Jan S.

doi:10.1016/j.cma.2022.115811

Cited by 36 publications

(13 citation statements)

References 44 publications

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“…Indeed FF networks lack the capability to retain memory across time steps, and thus they are unable to preserve the temporal dependency within the data. We refer to [62] for further discussions on these aspects.…”

Section: (C) the Need Of Lstm Networkmentioning

confidence: 99%

“…LSTM models have been shown to be effective in time series analysis, e.g. in speech recognition [58,59], natural language processing [60] and computational mechanics [61,62]. In particular, LSTM networks have proven to be successful in the detection of both long-and short-term temporal patterns and nonlinear correlations between datasets, with potential relevance in the construction of non-intrusive reduced order models [55,[63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, LSTM networks have proven to be successful in the detection of both long-and short-term temporal patterns and nonlinear correlations between datasets, with potential relevance in the construction of non-intrusive reduced order models [55,[63][64][65][66]. A recent work [62] has also shown their success in MF surrogate modelling for simultaneous parametric generalization and temporal forecast. Thus, instead of relying on expensive HF fullorder evaluations, MF-POD allows for efficient online approximation of solution fields over time and parameter variation by running fast LF simulations and then mapping their POD coefficients to the HF level.…”

Section: Introductionmentioning

confidence: 99%

“…Figure3. The visualization of an LSTM unit with its input-output setting[62,71].Since LSTM units are recurrent NNs that deal with sequential data, in practice, training data are grouped in batch subsequences with shape n batch × K × N POD , in which n batch is the batch size and K is the length of batch subsequences. To determine the NN model's hyperparameters, including the network architecture (i.e.…”

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confidence: 99%

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Multi-fidelity reduced-order surrogate modelling

Conti,

Guo,

Manzoni

et al. 2024

Proc. R. Soc. A.

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High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity data are scarce. However, low-fidelity models, while often displaying the qualitative solution behaviour, fail to accurately capture fine spatio-temporal and dynamic features of high-fidelity models. To address this shortcoming, we present a data-driven strategy that combines dimensionality reduction with multi-fidelity neural network surrogates. The key idea is to generate a spatial basis by applying proper orthogonal decomposition (POD) to high-fidelity solution snapshots, and approximate the dynamics of the reduced states—time-parameter-dependent expansion coefficients of the POD basis—using a multi-fidelity long short-term memory network. By mapping low-fidelity reduced states to their high-fidelity counterpart, the proposed reduced-order surrogate model enables the efficient recovery of full solution fields over time and parameter variations in a non-intrusive manner. The generality of this method is demonstrated by a collection of PDE problems where the low-fidelity model can be defined by coarser meshes and/or time stepping, as well as by misspecified physical features.

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Section: (C) the Need Of Lstm Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Multi-fidelity reduced-order surrogate modelling

Conti,

Guo,

Manzoni

et al. 2024

Proc. R. Soc. A.

Self Cite

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show abstract

“…Yan and Zhou [29] built an adaptive surrogate model based on the MF approach in conjunction with NN to solve the Bayesian inverse problem. The NN was used to bridge the low-and high-fidelity surrogate model in the framework of Markov chain Monte Carlo Conti et al [30] established the MF long shortterm memory networks to solve the time-dependent problems. Motamed [31] constructed two separate neural networks based on bi-fidelity training data.…”

Section: Introductionmentioning

confidence: 99%