Value Learning
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There is a content mismatch — the URL points to an arxiv paper titled 'Value Learning' relevant to AI alignment, but the retrieved content is from an unrelated lattice Boltzmann physics paper; metadata reflects the intended AI safety topic.
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Abstract
In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in \cite{2017_Otomo}. This improvement is achieved by controlling the relaxation time, modifying the equilibrium state, and employing more and higher lattice speeds, in a manner suggested by our analysis of the Taylor-series expansion method. The model's enhanced stability enables us to use larger time increments, thereby more than compensating for the extra computation required by the high lattice speeds. Furthermore, even though the time increments are larger than those of the previous scheme, the same level of accuracy is maintained because of the smaller truncation error of the new scheme. As a result, total performance with the new scheme on the D1Q7 lattice is improved by 92 $\%$ compared to the original scheme on the D1Q5 lattice.
Summary
This paper appears to be misidentified — the URL (arxiv 1711.03540) and title 'Value learning' suggest an AI safety paper on value learning, but the content retrieved is from an unrelated physics paper on lattice Boltzmann models. The metadata should reflect the intended AI safety topic of value learning, which concerns how AI systems can learn and align with human values.
Key Points
- •Value learning is a core AI alignment approach where AI systems infer human values from behavior rather than having values hard-coded
- •Key challenge: humans may not reliably demonstrate their true values, making inference difficult or misleading
- •Related to inverse reinforcement learning and the broader problem of specifying what humans actually want
- •Value learning must address value uncertainty, value complexity, and potential for manipulation of the learning process
- •Content mismatch: retrieved page content is a physics paper, not the intended AI safety resource
Cited by 1 page
| Page | Type | Quality |
|---|---|---|
| AI Alignment | Approach | 91.0 |
Cached Content Preview
[1711.03540] Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation
Efficient lattice Boltzmann models for the Kuramoto-Sivashinsky equation
Hiroshi Otomo
hiroshi.otomo@tufts.edu
Bruce M. Boghosian
Department of Mathematics, Tufts University, Medford, Massachusetts 02155, USA
François Dubois
CNAM Paris, Laboratoire de mécanique des structures et des systèmes couplés,
292, rue Saint-Martin, 75141 Paris cedex 03,France
Université Paris-Sud, Laboratoire de mathématiques, UMR CNRS 8628, 91405 Orsay cedex, France
Department of Mathematics, University Paris-Sud, Bat. 425, F-91405 Orsay, France
Abstract
In this work, we improve the accuracy and stability of the lattice Boltzmann model for the Kuramoto-Sivashinsky equation proposed in [ 1 ] . This improvement is achieved by controlling the relaxation time, modifying the equilibrium state, and employing more and higher lattice speeds, in a manner suggested by our analysis of the Taylor-series expansion method. The model’s enhanced stability enables us to use larger time increments, thereby more than compensating for the extra computation required by the high lattice speeds. Furthermore, even though the time increments are larger than those of the previous scheme, the same level of accuracy is maintained because of the smaller truncation error of the new scheme. As a result, total performance with the new scheme on the D1Q7 lattice is improved by 92 % percent \% compared to the original scheme on the D1Q5 lattice.
† † journal: Computers & \& fluids
1 Introduction
The Kuramoto-Sivashinsky (KS) equation is well known to reproduce a variety of chaotic phenomena caused by intrinsic instability such as the unstable behavior of laminar flame fronts [ 2 , 3 ] , thin-water-film flow on a vertical wall [ 4 ] , and persistent wave propagation through a reaction-diffusion system [ 5 ] .
For space X 𝑋 X and time T 𝑇 T , the KS equation for a quantity ρ 𝜌 \rho is
∂ T ρ + ρ ∂ X ρ = − ∂ X 2 ρ − ∂ X 4 ρ . subscript 𝑇 𝜌 𝜌 subscript 𝑋 𝜌 subscript superscript 2 𝑋 𝜌 subscript superscript 4 𝑋 𝜌 \partial_{T}\rho+\rho\partial_{X}\rho=-\partial^{2}_{X}\rho-\partial^{4}_{X}\rho.
(1)
The second term on the left-hand side is the nonlinear advection term, while the first and second terms on the right-hand side are the production and hyperdiffusion terms, respectively. Examining the relationship between those terms, Holmes [ 6 ] found that the KS equation exhibits basic properties of turbulent flow, and indeed corresponds to the equation for the fluctuating velocity derived from the Navier-Stokes equation. Accordingly, the KS equation is often used to explore basic features of chaotic systems.
The lattice Boltzmann (LB) method was originally developed from models of lattice-gas cellular automata, and is based on principles of kinetic theory [ 7 ] . The ensemble of particle states
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