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- Espath, Luis, et al.
(författare)
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Statistical learning for fluid flows : Sparse Fourier divergence-free approximations
- 2021
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Ingår i: Physics of fluids. - : AIP Publishing. - 1070-6631 .- 1089-7666. ; 33:9
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Tidskriftsartikel (refereegranskat)abstract
- We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L & nbsp;projection. Within this physics-informed type of statistical learning framework, we adaptively build a sparse set of Fourier basis functions with corresponding coefficients by solving a sequence of minimization problems where the set of basis functions is augmented greedily at each optimization problem. We regularize our minimization problems with the seminorm of the fractional Sobolev space in a Tikhonov fashion. In the Fourier setting, the incompressibility (divergence-free) constraint becomes a finite set of linear algebraic equations. We couple our spatial approximation with the truncated singular-value decomposition of the flow measurements for temporal compression. Our computational framework thus combines supervised and unsupervised learning techniques. We assess the capabilities of our method in various numerical examples arising in fluid mechanics.
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| 2. |
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| 3. |
- Kiessling, Jonas, et al.
(författare)
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A Computable Definition of the Spectral Bias
- 2022
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Ingår i: Proceedings of the 36th AAAI Conference on Artificial Intelligence, AAAI 2022. - : Association for the Advancement of Artificial Intelligence. ; 36:7, s. 7168-7175
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Konferensbidrag (refereegranskat)abstract
- Neural networks have a bias towards low frequency functions. This spectral bias has been the subject of several previous studies, both empirical and theoretical. Here we present a computable definition of the spectral bias based on a decomposition of the reconstruction error into a low and a high frequency component. The distinction between low and high frequencies is made in a way that allows for easy interpretation of the spectral bias. Furthermore, we present two methods for estimating the spectral bias. Method 1 relies on the use of the discrete Fourier transform to explicitly estimate the Fourier spectrum of the prediction residual, and Method 2 uses convolution to extract the low frequency components, where the convolution integral is estimated by Monte Carlo methods. The spectral bias depends on the distribution of the data, which is approximated with kernel density estimation when unknown. We devise a set of numerical experiments that confirm that low frequencies are learned first, a behavior quantified by our definition.
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| 4. |
- Kiessling, Jonas, et al.
(författare)
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Artificial Intelligence Outperforms Kaplan-Meier Analyses Estimating Survival after Elective Treatment of Abdominal Aortic Aneurysms
- 2023
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Ingår i: European Journal of Vascular and Endovascular Surgery. - : Elsevier BV. - 1078-5884 .- 1532-2165. ; 65:4, s. 600-607
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Tidskriftsartikel (refereegranskat)abstract
- Objective: Long term differences in survival after elective repair of abdominal aortic aneurysms (AAAs) between open surgical repair (OSR) and endovascular aneurysm repair (EVAR) are unclear, and hitherto artificial intelligence has not been used for this purpose. The aim was to compare the precision of survival estimates between the Kaplan -Meier (KM) method and the artificial intelligence derived method Neural Multi-Task Logistic Regression (N-MTLR), and to compare survival estimates as a function of patient age and time since surgery between OSR and EVAR using N-MTLR. Methods: All AAAs between 2003 and 2018 in Denmark were identified in the Danish vascular registry. Survival was estimated using the KM and N-MTLR methods, and prediction performance was estimated with the Brier score. Results: 7 912 patients were included in the study, n = 6 569 (83%) men, median age 72 years (range 35 -92), with a median follow-up time of 45.7 months (range 0 -120). The two treatment cohorts, OSR n = 5 495 (69%), and EVAR n = 2 417 (31%), differed significantly in patient characteristics. The Brier score for KM increased from 0.044 to 0.244, and for N-MTLR from 0.044 to 0.206, from 90 days to 10 years. The N-MTLR method was more accurate than KM from 90 days to 10 years after surgery, p < .025. N-MTLR demonstrated significant increased probability for survival for OSR in patients aged 58 -76 years at five years, and 65 -73 at 10 years after surgery, and the opposite was found for the benefit of EVAR in patients aged 72 -85 years at one year, 85 -90 years at five years, and for 85 -90 year olds at 10 years after surgery. Conclusion: N-MTLR outperforms KM for the entire post-operative follow-up time. This N-MTLR model has the potential to render more precise patient specific survival estimates and establish survival differences between subgroups of patients that KM is unable to detect, demonstrated here for different age groups.
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| 5. |
- Kiessling, Jonas, et al.
(författare)
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Wind field reconstruction with adaptive random Fourier features
- 2021
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 477:2255
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model beta(x)= Sigma(K)(k-1) beta(k) e(i omega kx) approximating the velocity field, with randomly sampled frequencies omega(k) and amplitudes beta(k) trained to minimize a loss function. We include a physically motivated divergence penalty vertical bar del. beta(x)vertical bar(2), as well as a penalty on the Sobolev norm of beta. We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive Metropolis-Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.
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| 6. |
- Lövgren, Tanja, et al.
(författare)
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Complete and long-lasting clinical responses in immune checkpoint inhibitor-resistant, metastasized melanoma treated with adoptive T cell transfer combined with DC vaccination
- 2020
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Ingår i: Oncoimmunology. - : TAYLOR & FRANCIS INC. - 2162-4011 .- 2162-402X. ; 9:1
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Tidskriftsartikel (refereegranskat)abstract
- Development of T cell-directed immune checkpoint inhibitors (ICI) has revolutionized metastatic melanoma (MM) therapy, but <50% of treated patients experience durable responses. This phase I trial (NCT01946373) investigates the safety/feasibility of tumor-infiltrating lymphocyte (TIL) adoptive cell therapy (ACT) combined with dendritic cell (DC) vaccination in MM patients progressing on ICI. An initial cohort (5 patients) received TIL therapy alone to evaluate safety and allow for optimization of TIL expansion protocols. A second cohort (first-in-man, 5 patients) received TIL combined with autologous tumor lysate-loaded DC vaccination. All patients received cyclophosphamide/fludarabine preconditioning prior to, and intravenous (i.v.) IL-2 after, TIL transfer. The DC vaccine was given as five intradermal injections after TIL and IL-2 administration. [F-18]-FDG PET/CT radiology was performed to evaluate clinical response, according to RECIST 1.1 (on the CT part). Immunological monitoring was performed by flow cytometry and T-cell receptor (TCR) sequencing. In the safety/optimization cohort, all patients had a mixed response or stable disease, but none durable. In the combination cohort, two patients experienced complete responses (CR) that are still ongoing (>36 and >18 months, respectively). In addition, two patients had partial responses (PR), one still ongoing (>42 months) with only a small bone-lesion remaining, and one of short duration (<4 months). One patient died early during treatment and did not receive DC. Long-lasting persistency of the injected TILs was demonstrated in blood. In summary, we report clinical responses by TIL therapy combined with DC vaccination in 4 out of 4 treated MM patients who previously failed ICI.
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