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]