Sensitivity-preserving of Fisher Information Matrix through random data down-sampling for experimental design

Christian Klingenberg; Kathrin Hellmuth; Qin Li

arxiv: 2409.15906 · v3 · submitted 2024-09-24 · 🧮 math.NA · cs.NA· math.OC

Sensitivity-preserving of Fisher Information Matrix through random data down-sampling for experimental design

Kathrin Hellmuth , Christian Klingenberg , Qin Li This is my paper

Pith reviewed 2026-05-23 21:02 UTC · model grok-4.3

classification 🧮 math.NA cs.NAmath.OC

keywords Fisher Information Matrixmatrix sketchingexperimental designinverse problemsdown-samplingsensor placementSchrödinger equationrandomized linear algebra

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The pith

A randomized sketching approach approximates the Fisher Information Matrix while preserving its sensitivity properties for experimental design.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that matrix sketching techniques can select a subset of experimental data that maintains the conditioning of the full Fisher Information Matrix. This is important because good parameter reconstruction in inverse problems relies on choosing data sensitive to the unknown parameters, but using all data can be computationally expensive. By sampling from a sensitivity-informed distribution with gradient-free methods, the method works even in non-smooth or discrete design spaces. Tests on reconstructing a Schrödinger potential demonstrate that optimal sensor locations can be found efficiently this way.

Core claim

The framework achieves a sensitivity-preserving approximation of the full-data Fisher Information Matrix by drawing samples from a sensitivity-informed distribution using gradient-free ensemble sampling methods from randomized numerical linear algebra, thereby enabling efficient down-sampling of experimental setups for robust inverse problem reconstructions.

What carries the argument

Matrix sketching of the data matrix drawn from a sensitivity-informed distribution, executed via gradient-free ensemble methods to handle non-smooth design spaces.

If this is right

The down-sampled data maintains the information content for parameter sensitivity.
Optimal experimental designs can be computed more efficiently.
The approach applies to discrete and non-smooth design spaces.
Reconstructions of unknown parameters remain of high quality with reduced data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This could reduce computational costs in large-scale inverse problems beyond the tested Schrödinger case.
It might integrate with other randomized algorithms for further efficiency.
Extensions to time-dependent or nonlinear inverse problems could be explored.

Load-bearing premise

That the sketched matrix obtained from samples of the sensitivity-informed distribution will have conditioning that reliably matches the full FIM across the design space.

What would settle it

An experiment where the condition number of the approximated FIM differs substantially from the full FIM for a chosen set of sensor locations in the Schrödinger problem.

Figures

Figures reproduced from arXiv: 2409.15906 by Christian Klingenberg, Kathrin Hellmuth, Qin Li.

**Figure 1.** Figure 1: Top row shows four different ground-truth media p∗, and the bottom row shows the optimal sampling distribution ˜π for each of them. System ground truth parameter A p A ∗ =   13.6 10 10 10 10 10 10 10 10   B p B ∗ =   5.856 0.103 3.168 3.7441 2.493 1.124 0.9902 3.803 0.846   C p C ∗ =   11 8.889 7.778 6.667 5.556 4.444 3.333 2.222 1.111   D p D ∗ =   10 0 0 0 0 0 0 0 0   [PITH_FULL_IMAGE:fi… view at source ↗

**Figure 2.** Figure 2: Optimal importance sampling distributions ˜µ for scaling parameters αp∗ with α = 0.1 (left), α = 1 (center) and α = 10 (right). The ground truth parameters p∗ from System C and D from [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 3.** Figure 3: Full Data Setup: Measurement locations (red dots) are located in all grid points. The optimal importance sampling distribution ˜µ is drawn in the background. − [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗

**Figure 4.** Figure 4: Red markers demonstrate the location of the sensors, with the background plotted as the optimal distribution. The left panel shows the distribution of the initial samples. The middle and the right panel show, respectively, the EKS and CBS samples after 25 iterations. The minimum eigenvalues of the FIM change from 1.48e−4 to 2.06 and 1.41 and the inverse condition numbers from order 1e−7 to 1e−3, ensuring l… view at source ↗

**Figure 5.** Figure 5: Evolution of minimum eigenvalue (solid lines) and deviation of the down-sampled FIMs from the full data setup in Frobenius norm (dashed lines). Three sampling methods are used: EKS (blue), CBS (orange) and repeated sampling from the initial guess distribution (green), all used in greedy mode. Initial distribution is shared across three sampling methods. Design D λD min c D inv full data Dfull 0.8 8.18 · 10… view at source ↗

**Figure 6.** Figure 6: Uniformly distributed initial guess (upper left) of the distribution of the sensors (red dots) in the domain X, where the optimal importance sampling distribution is drawn in the background. Application of greedy EKS (lower left), CBS (lower left) and repeated sampling w.r.t. the uniform distribution changes the sensor distribution and dramatically increases the condition number and minimum eigenvalue of… view at source ↗

**Figure 7.** Figure 7: Optimal importance sampling distribution ˜µ (left) and shape of the ground truth parameter p∗ (right) in the two-dimensional setting [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

**Figure 8.** Figure 8: Loss landscapes (left) for different sensor locations (right): full data setup (first row) and normally distributed initial sensor locations (second row). 4.2. Source Term Design. In our second set of experiments, we allow the source term to be adjusted as well. In particular, we set: γ(x) = γ1x1 + γ2x2 + 10 , with ~γ = (γ1, γ2) ∈ [−2, 2]2 . Similar to the previous example, the possible measurements are t… view at source ↗

**Figure 9.** Figure 9: The top row shows the quadratic loss landscapes and the bottom row shows the locations of the samples with the background presenting the optimal distribution. The three panels are results from greedy versions of EKS, CBS and repeated normal sampling from initial guess distribution. The flexibility of x and ~γ means we have four dimension of design space: Ω = Ω ˆ ×[−2, 2]2 . We endow this space with µ, the… view at source ↗

**Figure 10.** Figure 10: Four different designs, characterized by their sensor locations given by the dot locations, and γ1, γ2 values encoded in colour and size of the dots, together with their sensitivity measures: normally distributed initial sensor location guess with uniformly distributed γ1, γ2 (upper left), greedy repeated sampling w.r.t. this distribution (upper right), greedy EKS (lower left) and CBS (lower right) w.r.t.… view at source ↗

read the original abstract

The quality of numerical reconstructions for unknown parameters in inverse problems depends fundamentally on the selection of experimental data. To ensure a robust reconstruction, it is crucial to select data that are sensitive to the parameters, a property typically characterized by the conditioning of the Fisher Information Matrix (FIM). In this work, we propose a general framework for an efficient down-sampling strategy that selects experimental setups that preserves the information content of the full-data FIM. Our approach leverages matrix sketching techniques from randomized numerical linear algebra to achieve a sensitivity-preserving approximation. The method involves drawing samples from a sensitivity-informed distribution, which we execute using gradient-free ensemble sampling methods to handle potentially non-smooth or discrete design spaces. Numerical experiments demonstrate the effectiveness of this framework in selecting optimal sensor locations for a Schroedinger potential reconstruction problem.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a sketching method to downsample data for inverse problems while trying to keep the Fisher Information Matrix well-conditioned.

read the letter

The main takeaway is a framework that combines matrix sketching from randomized linear algebra with gradient-free ensemble sampling to pick a smaller set of experimental points whose FIM approximation stays close to the full-data version in conditioning. They apply it to sensor placement for Schrödinger potential recovery. The new element is the specific pairing of sensitivity-informed sampling (via ensembles that avoid gradients) with sketching to handle non-smooth or discrete design spaces. Prior work on sketching exists, but this targets FIM preservation directly in experimental design. It does a clean job linking established tools to this setting and keeps the method general rather than problem-specific. The Schrödinger test at least shows the approach can be run on a concrete inverse problem. One soft spot is the lack of reported numbers in the abstract: no error tables, no baseline comparisons, and no quantification of how much conditioning is actually preserved or lost. That makes it hard to judge whether the approximation holds reliably or only under favorable choices. The central assumption—that samples from the sensitivity distribution will produce a sketched matrix whose properties track the full FIM across the space—needs the numerics to back it up, and those details are not visible here. This is for people working on numerical inverse problems and optimal design who already know FIM conditioning and want a cheaper way to select data. A reader focused on practical down-sampling in parameter estimation would get value. It deserves a serious referee because the idea is grounded and the application area is active, even if the empirical section needs more substance to carry the claim.

Referee Report

0 major / 2 minor

Summary. The manuscript proposes a general framework for efficient down-sampling of experimental data that preserves the conditioning of the full-data Fisher Information Matrix (FIM) in inverse problems. The method applies matrix sketching techniques from randomized numerical linear algebra, drawing samples from a sensitivity-informed distribution via gradient-free ensemble sampling methods to accommodate non-smooth or discrete design spaces. Effectiveness is demonstrated through numerical experiments on optimal sensor location selection for a Schrödinger potential reconstruction problem.

Significance. If the approximation reliably preserves FIM conditioning, the framework could enable scalable experimental design for large inverse problems by reducing computational cost while maintaining sensitivity information, extending established sketching methods to this setting.

minor comments (2)

The abstract states that numerical experiments demonstrate effectiveness but provides no quantitative metrics, error analysis, baselines, or conditioning comparisons; this should be addressed in the results section to allow verification of the preservation claim.
Clarify the precise definition of 'sensitivity-preserving' (e.g., via a specific norm or eigenvalue bound on the sketched vs. full FIM) and how it is measured in the experiments.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive summary of our manuscript, as well as the recommendation for minor revision. The referee's description accurately reflects the proposed matrix-sketching framework for preserving FIM conditioning via sensitivity-informed sampling.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies established matrix sketching techniques from randomized numerical linear algebra to approximate the Fisher Information Matrix while preserving sensitivity. The central framework draws samples from a sensitivity-informed distribution using gradient-free ensemble methods and demonstrates effectiveness via numerical experiments on the Schrödinger problem. No load-bearing steps reduce by the paper's own equations to fitted inputs, self-definitions, or self-citation chains; the approach is positioned as leveraging external RLA methods without renaming known results or smuggling ansatzes. This qualifies as self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields an incomplete ledger; no explicit free parameters or invented entities are named, and the work relies on standard properties of the Fisher Information Matrix and randomized linear algebra without introducing new postulates.

axioms (2)

domain assumption The conditioning of the Fisher Information Matrix characterizes the sensitivity of measurements to unknown parameters in inverse problems.
Invoked in the opening sentences of the abstract as the foundation for data selection.
domain assumption Matrix sketching from randomized numerical linear algebra can produce a sensitivity-preserving approximation of a given matrix.
Central to the proposed framework as stated in the abstract.

pith-pipeline@v0.9.0 · 5671 in / 1402 out tokens · 28118 ms · 2026-05-23T21:02:35.363656+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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Cost.FunctionalEquation washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Our approach leverages matrix sketching techniques from randomized numerical linear algebra to achieve a sensitivity-preserving approximation of the full-data Fisher Information Matrix.
Foundation.RealityFromDistinction reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Theorem 1. ... π(u) ≥ β ||A_u,:||_2^2 / ||A||_F^2 ... P(||A^TA - C^TC||_F ≤ ... ) ≥ 1-δ

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matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

[1]

Alexanderian

A. Alexanderian. Optimal experimental design for inﬁni te-dimensional bayesian inverse problems gov- erned by pdes: A review. Inverse Problems , 37, 01 2021

work page 2021
[2]

Attia and E

A. Attia and E. Constantinescu. Optimal experimental de sign for inverse problems in the presence of observation correlations. SIAM Journal on Scientiﬁc Computing , 44(4):A2808–A2842, 2022

work page 2022
[3]

Bandara, J

S. Bandara, J. P. Schl¨ oder, R. Eils, H. G. Bock, and T. Mey er. Optimal experimental design for parameter estimation of a cell signaling model. PLoS computational biology , 5(11):e1000558, 2009

work page 2009
[4]

Bou-Rabee and M

N. Bou-Rabee and M. Hairer. Nonasymptotic mixing of the m ala algorithm. IMA Journal of Numerical Analysis, 33(1):80–110, 2013. SENSITIVITY PRESER VING SAMPLING OF THE FISHER-INFORMATIO N MATRIX 23

work page 2013
[5]

Boull´ e, D

N. Boull´ e, D. Halikias, and A. Townsend. Elliptic pde le arning is provably data-eﬃcient. Proceedings of the National Academy of Sciences , 120(39):e2303904120, 2023

work page 2023
[6]

Boull´ e and A

N. Boull´ e and A. Townsend. Learning elliptic partial di ﬀerential equations with randomized linear algebra. Found. Comput. Math. , 23(2):709–739, 2023

work page 2023
[7]

Bui-Thanh, Q

T. Bui-Thanh, Q. Li, and L. Zepeda-N´ u˜ nez. Bridging and improving theoretical and computa- tional electrical impedance tomography via data completio n. SIAM Journal on Scientiﬁc Computing , 44(3):B668–B693, 2022

work page 2022
[8]

J. A. Carrillo, F. Hoﬀmann, A. M. Stuart, and U. Vaes. Cons ensus-based sampling. Studies in Applied Mathematics, 148(3):1069–1140, 2022

work page 2022
[9]

T. Chen, E. Fox, and C. Guestrin. Stochastic gradient ham iltonian monte carlo. In International conference on machine learning , pages 1683–1691. PMLR, 2014

work page 2014
[10]

Y. Chen, B. Hosseini, H. Owhadi, and A. M. Stuart. Solvin g and learning nonlinear pdes with gaussian processes. Journal of Computational Physics , 447:110668, 2021

work page 2021
[11]

Cheng, N

X. Cheng, N. S. Chatterji, P. L. Bartlett, and M. I. Jorda n. Underdamped langevin mcmc: A non- asymptotic analysis. In Conference on learning theory , pages 300–323. PMLR, 2018

work page 2018
[12]

Chung, M

J. Chung, M. Chung, and J. T. Slagel. Iterative sampled m ethods for massive and separable nonlinear inverse problems. In Scale Space and Variational Methods in Computer Vision: 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30–July 4 , 2019, Proceedings 7 , pages 119–130. Springer, 2019

work page 2019
[13]

A. S. Dalalyan and A. Karagulyan. User-friendly guaran tees for the langevin monte carlo with inac- curate gradient. Stochastic Processes and their Applications , 129(12):5278–5311, 2019

work page 2019
[14]

Ding and Q

Z. Ding and Q. Li. Ensemble kalman sampler: Mean-ﬁeld li mit and convergence analysis. SIAM Journal on Mathematical Analysis , 53(2):1546–1578, 2021

work page 2021
[15]

Dong and Y

S. Dong and Y. Wang. A method for computing inverse param etric pde problems with random-weight neural networks. Journal of Computational Physics , 489:112263, 2023

work page 2023
[16]

Dwivedi, Y

R. Dwivedi, Y. Chen, M. J. Wainwright, and B. Yu. Log-con cave sampling: Metropolis-hastings algorithms are fast. Journal of Machine Learning Research , 20(183):1–42, 2019

work page 2019
[17]

Evensen, F

G. Evensen, F. C. Vossepoel, and P. J. Van Leeuwen. Data assimilation fundamentals: A uniﬁed formulation of the state and parameter estimation problem . Springer Nature, 2022

work page 2022
[18]

Garbuno-Inigo, F

A. Garbuno-Inigo, F. Hoﬀmann, W. Li, and A. M. Stuart. In teracting langevin diﬀusions: Gradient structure and ensemble kalman sampler. SIAM Journal on Applied Dynamical Systems , 19(1):412–441, 2020

work page 2020
[19]

X. Huan, J. Jagalur, and Y. Marzouk. Optimal experiment al design: Formulations and computations, 2024

work page 2024
[20]

Huang and S

Z. Huang and S. Becker. Spectral estimation from simula tions via sketching. Journal of Computational Physics, 447:110686, 2021

work page 2021
[21]

R. Jin, Q. Li, A. Nair, and S. Stechmann. Unique reconstr uction for discretized inverse problems: a random sketching approach via subsampling, 2024

work page 2024
[22]

J. Kiefer. Optimum experimental designs. Journal of the Royal Statistical Society. Series B (Method- ological), 21(2):272–319, 1959

work page 1959
[23]

N. B. Kovachki and A. M. Stuart. Ensemble kalman inversi on: a derivative-free technique for machine learning tasks. Inverse Problems , 35(9):095005, aug 2019

work page 2019
[24]

M. W. Mahoney. Lecture notes on randomized linear algeb ra, 2016

work page 2016
[25]

Mangoubi and A

O. Mangoubi and A. Smith. Mixing of hamiltonian monte ca rlo on strongly log-concave distributions: Continuous dynamics. The Annals of Applied Probability , 31(5):2019–2045, 2021

work page 2019
[26]

Manohar, B

K. Manohar, B. W. Brunton, J. N. Kutz, and S. L. Brunton. D ata-driven sparse sensor placement for reconstruction: Demonstrating the beneﬁts of exploiti ng known patterns. IEEE Control Systems Magazine, 38(3):63–86, 2018

work page 2018
[27]

Martinsson and J

P.-G. Martinsson and J. A. Tropp. Randomized numerical linear algebra: Foundations and algorithms. Acta Numerica, 29:403–572, 2020

work page 2020
[28]

d- optimal

T. J. Mitchell. An algorithm for the construction of “d- optimal” experimental designs. Technometrics, 42(1):48–54, 2000

work page 2000
[29]

Nordebo, M

S. Nordebo, M. Gustafsson, A. Khrennikov, B. Nilsson, a nd J. Toft. Fisher information for inverse problems and trace class operators. Journal of mathematical physics , 53(12), 2012

work page 2012
[30]

Orozco, F

R. Orozco, F. J. Herrmann, and P. Chen. Probabilistic ba yesian optimal experimental design using conditional normalizing ﬂows. arXiv preprint arXiv:2402.18337 , 2024. 24 SENSITIVITY PRESER VING SAMPLING OF THE FISHER-INFORMAT ION MATRIX

work page arXiv 2024
[31]

S. Park, D. Kato, Z. Gima, R. Klein, and S. Moura. Optimal experimental design for parameterization of an electrochemical lithium-ion battery model. Journal of The Electrochemical Society, 165(7):A1309, 2018

work page 2018
[32]

S. Reich. A dynamical systems framework for intermitte nt data assimilation. BIT Numerical Mathe- matics, 51:235–249, 2011

work page 2011
[33]

Riedl, T

K. Riedl, T. Klock, C. Geldhauser, and M. Fornasier. Gra dient is all you need?, 2023

work page 2023
[34]

G. O. Roberts and R. L. Tweedie. Exponential convergenc e of langevin distributions and their discrete approximations. Bernoulli, 2(4):341–363, 1996

work page 1996
[35]

Shun and P

Z. Shun and P. McCullagh. Laplace approximation of high dimensional integrals. Journal of the Royal Statistical Society Series B: Statistical Methodology , 57(4):749–760, 1995

work page 1995
[36]

Sprungk, S

B. Sprungk, S. Weissmann, and J. Zech. Metropolis-adju sted interacting particle sampling, 2023

work page 2023
[37]

U. Vaes. Sharp propagation of chaos for the ensemble lan gevin sampler, 2024

work page 2024
[38]

D. P. Woodruﬀ et al. Sketching as a tool for numerical lin ear algebra. Foundations and Trends ® in Theoretical Computer Science , 10(1–2):1–157, 2014

work page 2014
[39]

J. J. Ye and J. Zhou. Minimizing the condition number to c onstruct design points for polynomial regression models. SIAM Journal on Optimization , 23(1):666–686, 2013

work page 2013

[1] [1]

Alexanderian

A. Alexanderian. Optimal experimental design for inﬁni te-dimensional bayesian inverse problems gov- erned by pdes: A review. Inverse Problems , 37, 01 2021

work page 2021

[2] [2]

Attia and E

A. Attia and E. Constantinescu. Optimal experimental de sign for inverse problems in the presence of observation correlations. SIAM Journal on Scientiﬁc Computing , 44(4):A2808–A2842, 2022

work page 2022

[3] [3]

Bandara, J

S. Bandara, J. P. Schl¨ oder, R. Eils, H. G. Bock, and T. Mey er. Optimal experimental design for parameter estimation of a cell signaling model. PLoS computational biology , 5(11):e1000558, 2009

work page 2009

[4] [4]

Bou-Rabee and M

N. Bou-Rabee and M. Hairer. Nonasymptotic mixing of the m ala algorithm. IMA Journal of Numerical Analysis, 33(1):80–110, 2013. SENSITIVITY PRESER VING SAMPLING OF THE FISHER-INFORMATIO N MATRIX 23

work page 2013

[5] [5]

Boull´ e, D

N. Boull´ e, D. Halikias, and A. Townsend. Elliptic pde le arning is provably data-eﬃcient. Proceedings of the National Academy of Sciences , 120(39):e2303904120, 2023

work page 2023

[6] [6]

Boull´ e and A

N. Boull´ e and A. Townsend. Learning elliptic partial di ﬀerential equations with randomized linear algebra. Found. Comput. Math. , 23(2):709–739, 2023

work page 2023

[7] [7]

Bui-Thanh, Q

T. Bui-Thanh, Q. Li, and L. Zepeda-N´ u˜ nez. Bridging and improving theoretical and computa- tional electrical impedance tomography via data completio n. SIAM Journal on Scientiﬁc Computing , 44(3):B668–B693, 2022

work page 2022

[8] [8]

J. A. Carrillo, F. Hoﬀmann, A. M. Stuart, and U. Vaes. Cons ensus-based sampling. Studies in Applied Mathematics, 148(3):1069–1140, 2022

work page 2022

[9] [9]

T. Chen, E. Fox, and C. Guestrin. Stochastic gradient ham iltonian monte carlo. In International conference on machine learning , pages 1683–1691. PMLR, 2014

work page 2014

[10] [10]

Y. Chen, B. Hosseini, H. Owhadi, and A. M. Stuart. Solvin g and learning nonlinear pdes with gaussian processes. Journal of Computational Physics , 447:110668, 2021

work page 2021

[11] [11]

Cheng, N

X. Cheng, N. S. Chatterji, P. L. Bartlett, and M. I. Jorda n. Underdamped langevin mcmc: A non- asymptotic analysis. In Conference on learning theory , pages 300–323. PMLR, 2018

work page 2018

[12] [12]

Chung, M

J. Chung, M. Chung, and J. T. Slagel. Iterative sampled m ethods for massive and separable nonlinear inverse problems. In Scale Space and Variational Methods in Computer Vision: 7th International Conference, SSVM 2019, Hofgeismar, Germany, June 30–July 4 , 2019, Proceedings 7 , pages 119–130. Springer, 2019

work page 2019

[13] [13]

A. S. Dalalyan and A. Karagulyan. User-friendly guaran tees for the langevin monte carlo with inac- curate gradient. Stochastic Processes and their Applications , 129(12):5278–5311, 2019

work page 2019

[14] [14]

Ding and Q

Z. Ding and Q. Li. Ensemble kalman sampler: Mean-ﬁeld li mit and convergence analysis. SIAM Journal on Mathematical Analysis , 53(2):1546–1578, 2021

work page 2021

[15] [15]

Dong and Y

S. Dong and Y. Wang. A method for computing inverse param etric pde problems with random-weight neural networks. Journal of Computational Physics , 489:112263, 2023

work page 2023

[16] [16]

Dwivedi, Y

R. Dwivedi, Y. Chen, M. J. Wainwright, and B. Yu. Log-con cave sampling: Metropolis-hastings algorithms are fast. Journal of Machine Learning Research , 20(183):1–42, 2019

work page 2019

[17] [17]

Evensen, F

G. Evensen, F. C. Vossepoel, and P. J. Van Leeuwen. Data assimilation fundamentals: A uniﬁed formulation of the state and parameter estimation problem . Springer Nature, 2022

work page 2022

[18] [18]

Garbuno-Inigo, F

A. Garbuno-Inigo, F. Hoﬀmann, W. Li, and A. M. Stuart. In teracting langevin diﬀusions: Gradient structure and ensemble kalman sampler. SIAM Journal on Applied Dynamical Systems , 19(1):412–441, 2020

work page 2020

[19] [19]

X. Huan, J. Jagalur, and Y. Marzouk. Optimal experiment al design: Formulations and computations, 2024

work page 2024

[20] [20]

Huang and S

Z. Huang and S. Becker. Spectral estimation from simula tions via sketching. Journal of Computational Physics, 447:110686, 2021

work page 2021

[21] [21]

R. Jin, Q. Li, A. Nair, and S. Stechmann. Unique reconstr uction for discretized inverse problems: a random sketching approach via subsampling, 2024

work page 2024

[22] [22]

J. Kiefer. Optimum experimental designs. Journal of the Royal Statistical Society. Series B (Method- ological), 21(2):272–319, 1959

work page 1959

[23] [23]

N. B. Kovachki and A. M. Stuart. Ensemble kalman inversi on: a derivative-free technique for machine learning tasks. Inverse Problems , 35(9):095005, aug 2019

work page 2019

[24] [24]

M. W. Mahoney. Lecture notes on randomized linear algeb ra, 2016

work page 2016

[25] [25]

Mangoubi and A

O. Mangoubi and A. Smith. Mixing of hamiltonian monte ca rlo on strongly log-concave distributions: Continuous dynamics. The Annals of Applied Probability , 31(5):2019–2045, 2021

work page 2019

[26] [26]

Manohar, B

K. Manohar, B. W. Brunton, J. N. Kutz, and S. L. Brunton. D ata-driven sparse sensor placement for reconstruction: Demonstrating the beneﬁts of exploiti ng known patterns. IEEE Control Systems Magazine, 38(3):63–86, 2018

work page 2018

[27] [27]

Martinsson and J

P.-G. Martinsson and J. A. Tropp. Randomized numerical linear algebra: Foundations and algorithms. Acta Numerica, 29:403–572, 2020

work page 2020

[28] [28]

d- optimal

T. J. Mitchell. An algorithm for the construction of “d- optimal” experimental designs. Technometrics, 42(1):48–54, 2000

work page 2000

[29] [29]

Nordebo, M

S. Nordebo, M. Gustafsson, A. Khrennikov, B. Nilsson, a nd J. Toft. Fisher information for inverse problems and trace class operators. Journal of mathematical physics , 53(12), 2012

work page 2012

[30] [30]

Orozco, F

R. Orozco, F. J. Herrmann, and P. Chen. Probabilistic ba yesian optimal experimental design using conditional normalizing ﬂows. arXiv preprint arXiv:2402.18337 , 2024. 24 SENSITIVITY PRESER VING SAMPLING OF THE FISHER-INFORMAT ION MATRIX

work page arXiv 2024

[31] [31]

S. Park, D. Kato, Z. Gima, R. Klein, and S. Moura. Optimal experimental design for parameterization of an electrochemical lithium-ion battery model. Journal of The Electrochemical Society, 165(7):A1309, 2018

work page 2018

[32] [32]

S. Reich. A dynamical systems framework for intermitte nt data assimilation. BIT Numerical Mathe- matics, 51:235–249, 2011

work page 2011

[33] [33]

Riedl, T

K. Riedl, T. Klock, C. Geldhauser, and M. Fornasier. Gra dient is all you need?, 2023

work page 2023

[34] [34]

G. O. Roberts and R. L. Tweedie. Exponential convergenc e of langevin distributions and their discrete approximations. Bernoulli, 2(4):341–363, 1996

work page 1996

[35] [35]

Shun and P

Z. Shun and P. McCullagh. Laplace approximation of high dimensional integrals. Journal of the Royal Statistical Society Series B: Statistical Methodology , 57(4):749–760, 1995

work page 1995

[36] [36]

Sprungk, S

B. Sprungk, S. Weissmann, and J. Zech. Metropolis-adju sted interacting particle sampling, 2023

work page 2023

[37] [37]

U. Vaes. Sharp propagation of chaos for the ensemble lan gevin sampler, 2024

work page 2024

[38] [38]

D. P. Woodruﬀ et al. Sketching as a tool for numerical lin ear algebra. Foundations and Trends ® in Theoretical Computer Science , 10(1–2):1–157, 2014

work page 2014

[39] [39]

J. J. Ye and J. Zhou. Minimizing the condition number to c onstruct design points for polynomial regression models. SIAM Journal on Optimization , 23(1):666–686, 2013

work page 2013