# Research

*"Chi cerca trova, chi ricerca ritrova" *

Ennio De Giorgi

To learn more about my research activity, check out my blog!

You can also find me on Google Scholar, ResearchGate, GitHub.

## Publications

### Preprints

1. S. Brugiapaglia, M. Liu, P. Tupper. *Invariance, encodings, and generalization: learning identity effects with neural networks* . Submitted, 2021. [arXiv] [GitHub]

### Refereed Book Chapters

2. S. Brugiapaglia. *A compressive spectral collocation method for the diffusion equation under the restricted isometry property.* In “Quantification of Uncertainty: Improving Efficiency and Technology”, series “**Lecture Notes in Computational Science and Engineering**”, vol. 137, Springer, Cham, 2020. [DOI] [arXiv] [GitHub]

1. B. Adcock, S. Brugiapaglia, C.G. Webster. *Compressed sensing approaches for polynomial approximation of high-dimensional functions.* In "Compressed Sensing and its Applications", series **Applied and Numerical Harmonic Analysis**, pp 93-124. Birkhäuser, Cham, 2018. [DOI] [arXiv]

### Refereed Journal Publications

11. B. Adcock, S. Brugiapaglia, M. King-Roskamp.* **The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees.* Accepted to IEEE Transactions on Signal Processing, vol. 69, pp. 3160-3175, 2021. [DOI] [arXiv]

10. B. Adcock, S. Brugiapaglia, M. King-Roskamp. *Do log factors matter? On optimal wavelet approximation and the foundations of compressed sensing.* **Foundations of Computational Mathematics**, to appear, 2021. [DOI] [arXiv]

9. S. Brugiapaglia, S. Dirksen, H.C. Jung, H. Rauhut. *Sparse recovery in bounded Riesz systems with applications to numerical methods for PDEs.* **Applied and Computational Harmonic Analysis**, 53, pp. 231-269, 2021. [DOI] [arXiv]

8. S. Brugiapaglia, L. Tamellini, M. Tani. *Compressive Isogeometric Analysis.* **Computers & Mathematics with Applications**, 80 (12), pp. 3137-3155, 2020. [DOI] [arXiv]

7. S. Brugiapaglia, S. Micheletti, F. Nobile, S. Perotto. *Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations.* **IMA Journal of Numerical Analysis**, draa036, 2020. [DOI] [arXiv] [Supplementary material] [GitHub]

6. B. Adcock, C. Boyer, S. Brugiapaglia. *On oracle-type local recovery guarantees in compressed sensing.* **Information and Inference: A Journal of the IMA**, iaaa007, 2020. [DOI] [arXiv] [GitHub]

5. B. Adcock, A. Bao, S. Brugiapaglia. *Correcting for unknown errors in sparse high-dimensional function approximation.* **Numerische Mathematik**, 142(3), pp. 667-711, 2019. [DOI] [arXiv]

4. S. Brugiapaglia, B. Adcock. *Robustness to Unknown Error in Sparse Regularization.* **IEEE Transactions on Information Theory**, 64 (10), pp. 6638-6661, 2018. [DOI] [arXiv]

3. S. Brugiapaglia, F. Nobile, S. Micheletti, S. Perotto. *A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems.* **Mathematics of Computation** 87 (309), pp. 1-38, 2018. [DOI] [ResearchGate]

2. S. Brugiapaglia, S. Micheletti, S. Perotto. *Compressed solving: A numerical approximation technique for elliptic PDEs based on Compressed Sensing. ***Computers & Mathematics with Applications**, 70 (6), pp. 1306–1335, 2015. [DOI] [ResearchGate]

1. S. Brugiapaglia, L. Gemignani. *On the simultaneous refinement of the zeros of H-palindromic polynomials.* **Journal of Computational and Applied Mathematics**, 272, pp. 293–303, 2014. [DOI] [ResearchGate]

### Refereed Conference Publications

5. B. Adcock, S. Brugiapaglia, N. Dexter, S. Moraga. *Learning High-Dimensional Hilbert-Valued Functions With Deep Neural Networks From Limited Data*. Proceedings of the AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences. Stanford, CA, USA, 2021.

4. B. Adcock, S. Brugiapaglia, N. Dexter, S. Moraga. *Deep Neural Networks Are Effective At Learning High-Dimensional Hilbert-Valued Functions From Limited Data*. Proceedings of Machine Learning Research vol 145:1–36, 2021, 2nd Annual Conference on Mathematical and Scientific Machine Learning. [paper] [arXiv]

3. S. Brugiapaglia, M. Liu, P. Tupper. *Generalizing Outside the Training Set: When Can Neural Networks Learn Identity Effects?* Proceedings of CogSci 2020. [arXiv] [GitHub]

2. B. Adcock, S. Brugiapaglia. *Sparse approximation of multivariate functions from small datasets via weighted orthogonal matching pursuit.* Proceedings of ICOSAHOM, 2018. [arXiv]

1. S. Brugiapaglia, B. Adcock, R.K. Archibald. *Recovery guarantees for compressed sensing with unknown error.* Proceedings of the 12th International Conference "Sampling Theory and Applications" (SampTA). Tallinn, Estonia, 2017. [DOI] [arXiv]

### Other Conference Publications

1. B. Adcock, S. Brugiapaglia, M. King-Roskamp. *Iterative and greedy algorithms for the sparsity in levels model in compressed sensing.* Proceedings of the Conference "SPIE Optical Engineering + Applications", San Diego, California, US, 2019. [DOI]

### Theses

3. *COmpRessed SolvING: Sparse Approximation of PDEs based on Compressed Sensing.* Ph.D. thesis, Politecnico di Milano, 2016. (Advisors: S. Perotto and S. Micheletti) [ResearchGate]

2. *Problemi non lineari agli autovalori per l'analisi della stabilità di equazioni differenziali con ritardo. *M.Sc. thesis, University of Pisa, 2012. (Advisor: L. Gemignani) [Academia.edu]

1. *Gli schemi di suddivisione: analisi della convergenza nel caso univariato stazionario. *B.Sc. thesis, University of Pisa, 2010. Advisor: D. Bini. [Academia.edu]