28 research outputs found
Kernel Methods are Competitive for Operator Learning
We present a general kernel-based framework for learning operators between
Banach spaces along with a priori error analysis and comprehensive numerical
comparisons with popular neural net (NN) approaches such as Deep Operator Net
(DeepONet) [Lu et al.] and Fourier Neural Operator (FNO) [Li et al.]. We
consider the setting where the input/output spaces of target operator
are reproducing kernel
Hilbert spaces (RKHS), the data comes in the form of partial observations
of input/output functions
(), and the measurement operators
and are linear. Writing and
for the optimal recovery maps
associated with and , we approximate with
where is an optimal
recovery approximation of . We show that, even when using vanilla
kernels (e.g., linear or Mat\'{e}rn), our approach is competitive in terms of
cost-accuracy trade-off and either matches or beats the performance of NN
methods on a majority of benchmarks. Additionally, our framework offers several
advantages inherited from kernel methods: simplicity, interpretability,
convergence guarantees, a priori error estimates, and Bayesian uncertainty
quantification. As such, it can serve as a natural benchmark for operator
learning.Comment: 35 pages, 10 figure
CMB-S4: Forecasting Constraints on Primordial Gravitational Waves
CMB-S4---the next-generation ground-based cosmic microwave background (CMB)
experiment---is set to significantly advance the sensitivity of CMB
measurements and enhance our understanding of the origin and evolution of the
Universe, from the highest energies at the dawn of time through the growth of
structure to the present day. Among the science cases pursued with CMB-S4, the
quest for detecting primordial gravitational waves is a central driver of the
experimental design. This work details the development of a forecasting
framework that includes a power-spectrum-based semi-analytic projection tool,
targeted explicitly towards optimizing constraints on the tensor-to-scalar
ratio, , in the presence of Galactic foregrounds and gravitational lensing
of the CMB. This framework is unique in its direct use of information from the
achieved performance of current Stage 2--3 CMB experiments to robustly forecast
the science reach of upcoming CMB-polarization endeavors. The methodology
allows for rapid iteration over experimental configurations and offers a
flexible way to optimize the design of future experiments given a desired
scientific goal. To form a closed-loop process, we couple this semi-analytic
tool with map-based validation studies, which allow for the injection of
additional complexity and verification of our forecasts with several
independent analysis methods. We document multiple rounds of forecasts for
CMB-S4 using this process and the resulting establishment of the current
reference design of the primordial gravitational-wave component of the Stage-4
experiment, optimized to achieve our science goals of detecting primordial
gravitational waves for at greater than , or, in the
absence of a detection, of reaching an upper limit of at CL.Comment: 24 pages, 8 figures, 9 tables, submitted to ApJ. arXiv admin note:
text overlap with arXiv:1907.0447
Snowmass 2021 CMB-S4 White Paper
This Snowmass 2021 White Paper describes the Cosmic Microwave Background Stage 4 project CMB-S4, which is designed to cross critical thresholds in our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. We provide an overview of the science case, the technical design, and project plan
CMB-S4
We describe the stage 4 cosmic microwave background ground-based experiment CMB-S4
CMB-S4: Forecasting Constraints on Primordial Gravitational Waves
Abstract: CMB-S4âthe next-generation ground-based cosmic microwave background (CMB) experimentâis set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2â3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5Ï, or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL
Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper
This is a solicited whitepaper for the Snowmass 2021 community planning exercise. The paper focuses on measurements and science with the Cosmic Microwave Background (CMB). The CMB is foundational to our understanding of modern physics and continues to be a powerful tool driving our understanding of cosmology and particle physics. In this paper, we outline the broad and unique impact of CMB science for the High Energy Cosmic Frontier in the upcoming decade. We also describe the progression of ground-based CMB experiments, which shows that the community is prepared to develop the key capabilities and facilities needed to achieve these transformative CMB measurements
Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper
International audienceThis is a solicited whitepaper for the Snowmass 2021 community planning exercise. The paper focuses on measurements and science with the Cosmic Microwave Background (CMB). The CMB is foundational to our understanding of modern physics and continues to be a powerful tool driving our understanding of cosmology and particle physics. In this paper, we outline the broad and unique impact of CMB science for the High Energy Cosmic Frontier in the upcoming decade. We also describe the progression of ground-based CMB experiments, which shows that the community is prepared to develop the key capabilities and facilities needed to achieve these transformative CMB measurements
Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper
This is a solicited whitepaper for the Snowmass 2021 community planning exercise. The paper focuses on measurements and science with the Cosmic Microwave Background (CMB). The CMB is foundational to our understanding of modern physics and continues to be a powerful tool driving our understanding of cosmology and particle physics. In this paper, we outline the broad and unique impact of CMB science for the High Energy Cosmic Frontier in the upcoming decade. We also describe the progression of ground-based CMB experiments, which shows that the community is prepared to develop the key capabilities and facilities needed to achieve these transformative CMB measurements