Tim Palmer

Abstract:

Most Earth-system simulations run on conventional central processing units in 64-bit double precision floating-point numbers Float64, although the need for high-precision calculations in the presence of large uncertainties has been questioned. Fugaku, currently the world's fastest supercomputer, is based on A64FX microprocessors, which also support the 16-bit low-precision format Float16. We investigate the Float16 performance on A64FX with ShallowWaters.jl, the first fluid circulation model that runs entirely with 16-bit arithmetic. The model implements techniques that address precision and dynamic range issues in 16 bits. The precision-critical time integration is augmented to include compensated summation to minimize rounding errors. Such a compensated time integration is as precise but faster than mixed precision with 16 and 32-bit floats. As subnormals are inefficiently supported on A64FX the very limited range available in Float16 is 6 × 10−5 to 65,504. We develop the analysis-number format Sherlogs.jl to log the arithmetic results during the simulation. The equations in ShallowWaters.jl are then systematically rescaled to fit into Float16, using 97% of the available representable numbers. Consequently, we benchmark speedups of up to 3.8x on A64FX with Float16. Adding a compensated time integration, speedups reach up to 3.6x. Although ShallowWaters.jl is simplified compared to large Earth-system models, it shares essential algorithms and therefore shows that 16-bit calculations are indeed a competitive way to accelerate Earth-system simulations on available hardware.

Abstract:

This paper draws on a number of Roger Penrose's ideas - including the non-Hamiltonian phase-space flow of the Hawking Box, conformal cyclic cosmology, non-computability, and gravitationally induced quantum state reduction - in order to propose a radically unconventional approach to quantum gravity: Invariant Set Theory (IST). In IST, the fundamental laws of physics describe the geometry of the phase portrait of the universe as a whole: "quantum"process is associated with fine-scale fractal geometry, "gravitational"process with larger-scale heterogeneous geometry. With this, it becomes possible to explain the experimental violation of Bell inequalities without having to abandon key ingredients of general relativity: determinism and local causality. Ensembles in IST can be described by complex Hilbert states over a finite set C p of complex numbers, where p is a large finite integer. The quantum mechanics of finite-dimensional Hilbert spaces is emergent as a singular limit when p → ∞. A small modification to the field equations of general relativity is proposed to make it consistent with IST.

Abstract:

The question of how humans have influenced individual extreme weather events is both scientifically and socially important. However, deficiencies in climate models’ representations of key mechanisms within the process chains that drive weather reduce our confidence in estimates of the human influence on extreme events. We propose that using forecast models that successfully predicted the event in question could increase the robustness of such estimates. Using a successful forecast means we can be confident that the model is able to faithfully represent the characteristics of the specific extreme event. We use this forecast-based methodology to estimate the direct radiative impact of increased CO2 concentrations (one component, but not the entirety, of human influence) on the European heatwave of February 2019.