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search.json

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     "title": "Differentiable and distributed Particle-Mesh n-body simulations",
     "section": "Traditional cosmological inference",
     "text": "Traditional cosmological inference\n\nBayesian inference in cosmology\n\nWe need to infer the cosmological parameters \\(\\theta\\) that generated an observartion \\(x\\)\n\n\\[p(\\theta | x ) \\propto \\underbrace{p(x | \\theta)}_{\\mathrm{likelihood}} \\ \\underbrace{p(\\theta)}_{\\mathrm{prior}}\\]\n\n\n\n\n\n\n\n\n\n\n ➢  Compute summary statistics based on the 2-point correlation function of the shear field\n\n\n ➢  Run an MCMC chain to recover the posterior distribution of the cosmological parameters, using an analytical likelihood\n\n\n\n\n\n\n\nLimitations\n\n\n\nSimple summary statistics assume Gaussianity\nThe need to compute an analytical likelihood"
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+    "href": "marseille2024/index.html#jax-automatic-differentiation-and-hardware-acceleration",
+    "title": "Differentiable and distributed Particle-Mesh n-body simulations",
+    "section": "JAX : Automatic differentiation and Hardware acceleration",
+    "text": "JAX : Automatic differentiation and Hardware acceleration\n\n     \nimport numpy as np\n\n\ndef multiply_and_add(a, b, c):\n    return np.dot(a, b) + c\n\n\na, b, c = np.random.normal(size=(3, 32, 32))\nresult = multiply_and_add(a, b, c)\n\n\nimport jax\nimport jax.numpy as jnp\n\n\ndef multiply_and_add(a, b, c):\n    return jnp.dot(a, b) + c\n\n\nkey = jax.random.PRNGKey(0)\na, b, c = jax.random.normal(key, (3, 32, 32))\n\nresult = multiply_and_add(a, b, c)"
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+    "objectID": "marseille2024/index.html#jax-automatic-differentiation-and-hardware-acceleration-1",
+    "href": "marseille2024/index.html#jax-automatic-differentiation-and-hardware-acceleration-1",
+    "title": "Differentiable and distributed Particle-Mesh n-body simulations",
+    "section": "JAX : Automatic differentiation and Hardware acceleration",
+    "text": "JAX : Automatic differentiation and Hardware acceleration\n\n     \nimport jax\nimport jax.numpy as jnp\n\n\ndef multiply_and_add(a, b, c):\n    return jnp.dot(a, b) + c\n\n\nkey = jax.random.PRNGKey(0)\na, b, c = jax.random.normal(key, (3, 32, 32))\n\nresult = multiply_and_add(a, b, c)"
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+    "objectID": "marseille2024/index.html#jax-automatic-differentiation-and-hardware-acceleration-2",
+    "href": "marseille2024/index.html#jax-automatic-differentiation-and-hardware-acceleration-2",
+    "title": "Differentiable and distributed Particle-Mesh n-body simulations",
+    "section": "JAX : Automatic differentiation and Hardware acceleration",
+    "text": "JAX : Automatic differentiation and Hardware acceleration\n\n     \nimport jax\nimport jax.numpy as jnp\n\n@jax.jit\ndef multiply_and_add(a, b, c):\n    return jnp.dot(a, b) + c\n\n\nkey = jax.random.PRNGKey(0)\na, b, c = jax.random.normal(key, (3, 32, 32))\n\nresult = multiply_and_add(a, b, c) \ngradient = jax.grad(multiply_and_add)(a, b, c)\n \n\n\nJAX : Numpy + Autograd + GPU\n\n\n\njax.grad uses automatic differentiation to compute the gradient of the function\njax.jit compiles the function to run on GPUs"
   }
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