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"Walk, Walk, Walk": Identifying Computational Thinking in Embodied Models Through Movement
- Award ID(s):
- 2112635
- PAR ID:
- 10475044
- Publisher / Repository:
- Proceedings of the Annual Meeting of the American Educational Research Association 2023.
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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ABSTRACT We examine a dynamic disclosure model in which the value of a firm follows a random walk. Every period, with some probability, the manager learns the firm's value and decides whether to disclose it. The manager maximizes the market perception of the firm's value, which is based on disclosed information. In equilibrium, the manager follows a threshold strategy with thresholds below current prices. He sometimes reveals pessimistic information that reduces the market perception of the firm's value. He does so to reduce future market uncertainty, which is valuable even under risk‐neutrality.more » « less
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We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at arbitrary points, without performing a global solve or constructing a volumetric grid or mesh. The method is hence well suited to inverse problems with complex geometry, such as PDE-constrained shape optimization. Like other walk on spheres (WoS) algorithms, our method is trivial to parallelize, and is agnostic to boundary representation (meshes, splines, implicit surfaces, etc.), supporting large topological changes. We focus in particular on screened Poisson equations, which model diverse problems from scientific and geometric computing. As in differentiable rendering, we jointly estimate derivatives with respect to all parameters—hence, cost does not grow significantly with parameter count. In practice, even noisy derivative estimates exhibit fast, stable convergence for stochastic gradient-based optimization, as we show through examples from thermal design, shape from diffusion, and computer graphics.more » « less
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We introduce a Monte Carlo method for computing derivatives of the solution to a partial differential equation (PDE) with respect to problem parameters (such as domain geometry or boundary conditions). Derivatives can be evaluated at arbitrary points, without performing a global solve or constructing a volumetric grid or mesh. The method is hence well suited to inverse problems with complex geometry, such as PDE-constrained shape optimization. Like otherwalk on spheres (WoS)algorithms, our method is trivial to parallelize, and is agnostic to boundary representation (meshes, splines, implicit surfaces,etc.), supporting large topological changes. We focus in particular on screened Poisson equations, which model diverse problems from scientific and geometric computing. As in differentiable rendering, we jointly estimate derivatives with respect to all parameters---hence, cost does not grow significantly with parameter count. In practice, even noisy derivative estimates exhibit fast, stable convergence for stochastic gradient-based optimization, as we show through examples from thermal design, shape from diffusion, and computer graphics.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.3102/2012668
