Pith Number

pith:YAVSXEKD

pith:2026:YAVSXEKDAO3RESJKVXDLHAPRTJ

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A numerical study into neural network surrogate model performance for uncertainty propagation

Kirubel Teferra, Noah Wade

Neural network surrogates for stochastic heat conduction exhibit order-of-magnitude larger errors at distribution tails due to extrapolation.

arxiv:2605.16078 v1 · 2026-05-15 · stat.ML · cs.LG

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Record completeness

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4 Citations open

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Claims

C1strongest claim

Among the models considered, the fully connected neural network trained using a weak form residual loss performs best in handling these extrapolated inputs, achieving the highest prediction accuracy for the numerically produced datasets.

C2weakest assumption

The generated training datasets adequately cover the probability space of the stochastic source term so that observed errors on extreme samples can be attributed primarily to extrapolation rather than other factors such as optimization failure or insufficient model capacity.

C3one line summary

Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.

References

47 extracted · 47 resolved · 3 Pith anchors

[1] I. E. Lagaris, A. Likas, D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, IEEE Transactions on Neural Networks 9 (1998) 987–1000 1998

[2] M. Raissi, P. Perdikaris, G. Karniadakis, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, Journ 2019 · doi:10.1016/j.jcp.2018.10.045

[3] S. Cai, Z. Wang, S. Wang, P. Perdikaris, G. E. Karniadakis, Physics-informed neural networks for heat transfer problems, Journal of Heat Transfer 143 (2021) 2021

[4] N. Sukumar, A. Srivastava, Exact imposition of boundary conditions with distance functions in physics- informed deep neural networks, Computer Methods in Applied Mechanics and Engineering 389 (2022) 1 2022

[5] R. Xu, D. Zhang, M. Rong, N. Wang, Weak form theory-guided neural network (TgNN-wf) for deep learning of subsurface single- and two-phase flow, Journal of Computational Physics 436 (2021) 110318. doi: 2021 · doi:10.1016/j.jcp.2021.110318

Receipt and verification

First computed	2026-05-20T00:01:51.675377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c02b2b914303b712492aadc6b381f19a762c81811d823eb060a9bfa95a586135

Aliases

arxiv: 2605.16078 · arxiv_version: 2605.16078v1 · doi: 10.48550/arxiv.2605.16078 · pith_short_12: YAVSXEKDAO3R · pith_short_16: YAVSXEKDAO3RESJK · pith_short_8: YAVSXEKD

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/YAVSXEKDAO3RESJKVXDLHAPRTJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c02b2b914303b712492aadc6b381f19a762c81811d823eb060a9bfa95a586135

Canonical record JSON

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    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-15T15:39:52Z",
    "title_canon_sha256": "3e5a5f65e21f568765f6b720cb6d6ab10ec64e0078ee74a77c0782d8750f288f"
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